Defoe and Connolly stamped their class on the game - watched by 13,715 - by scoring one apiece in the first 14 minutes as Hammers seized the initiative.
And though Lowe gave the second division visitors brief hope before half-time by hammering a free-kick past David James and into the top corner, the outstanding Connolly popped up to seal the win in the 79th minute.
The only concern for Hammers was the fitness of Anton Ferdinand, whose competitive home debut ended when he was stretchered off after suffering an ankle injury in a penalty box collision midway through the second half. He has gone to hospital for an x-ray and Hammers hope it's just a sprain, although the young right-back is likely to miss Saturday's opening home first division clash with Sheffield United.
Connolly, granted his wish to start following his outburst after scoring the winner at Deepdale, grabbed his chance with both hands again. Like a modern-day Pop Robson or Paul Goddard, he spins off his marker well to receive passes and spread the play wide. His intelligent movement and close control were a feature of the match.
Not that Connolly and Defoe received much supply from either Matt Etherington or Youssef Sofiane, making his first start, who provided little in the way of crosses, but the little Irish international was good enough to set up most of his chances for himself. Like the first goal.
With vision and impudence, Connolly attempted to chip Rushden keeper Turley from outside the box in the 10th minute. His audacity deserved a goal and though his shot struck the underside of the bar, Defoe was first on the scene to thump the rebound over the line from close range.
Connolly was trying to set up Defoe four minutes later but gladly controlled the ricochet before striding forward and tucking his left-footed shot just inside the bottom far corner.
Rushden, promoted from the third division last season, looked out of their depth until Lowe's free-kick reduced the arrears in the 34th minute, visibly lifting the visitors' spirits as the first half closed. They enjoyed more of the possession but lacked penetration in the final third.
Brian Talbot's side made most of the running immediately after the break, too, reducing Hammers to half-chances from Connolly and Defoe, whose neat combinations in attack provided the classiest moments of the night. Richard Garcia swept one long-range shot just over the angle after replacing the subdued Sofiane on the right, but it was inevitably the Defoe/Connolly combination that made all the difference again.
Defoe was unfortunate not to score himself after swivelling to hit a shot that the keeper could only parry to Connolly who, like all good goal poachers, was on the spot for an easy tap-in inside the six-yard box.
Manager Glenn Roeder praised his twin strikeforce but had words of encouragement, too, for Neil Mellor, who remained on the bench despite starting the Preston game instead of Connolly. Roeder says: "Neil has impressed me greatly since I've seen him in training - he has been brought up the right way at Liverpool and by his dad, who was a good player, too."
Of Defoe and all the constant transfer speculation surrounding Hammers' biggest asset, Roeder added: "He has conducted himself very well in training, in the media and with his attitude."
Having waited until January last season to record their first home win, Hammers safely managed to avoid another League Cup embarrassment in front of their own fans. Sheffield United on Saturday, though, will be much tougher as attention refocuses on vital league points.
By Tony McDonald
Minute by Minute:
2 - A searing burst of pace sees Sofiane escape down the right, but his cross is just inches too high for the head of Connolly.
5 - A speculative shot from Jamaican midfielder Paul Hall flies well wide of David James' goal.
6 - Hammers go close to opening the scoring, as Connolly's cut-back from the right is met by Sofiane, whose left-foot effort is heading for the bottom corner until Rushden keeper Turley sticks out a leg to divert it back out, where Sofiane is beaten to the ball by a defender.
10 - GOAL! Hammers take the lead, and again it's the Connolly-Defoe combination that pays dividends for Glenn Roeder's team. After Sofiane's cross is blocked, Connolly catches out Turley with a delightful feigned chip from the edge of the penalty area that bounces back off the crossbar into the six-yard box, where chief predator Defoe is on hand to slam the ball home. West Ham United 1 Rushden & Diamonds 0.
14 - GOAL! A second for the Hammers, and this time Connolly is the one to finish off his excellent approach play. After attempting to release Defoe - who is denied by a defender - the Irish striker picks up the loose ball and sends two defenders the wrong way with a clever turn before planting the ball low inside the bottom corner of the net. West Ham United 2 Rushden & Diamonds 0.
22 - After some neat build-up play, Brevett's slide-rule pass releases Etherington, whose unselfish pass almost picks out Connolly, but a Rushden defender slides in to clear.
25 - Mills' fierce low shot from 25 yards out is parried by James, but no-one in a Rushden shirt is near enough to collect the rebound.
26 - Hunter booked for foul on Connolly.
26 - After collecting a pass from Lee, Connolly unleashes a blistering left-foot shot that Turley does well to hold close to his right hand post.
32 - Connolly and Defoe - causing Rushden all kinds of problems - combine again as the England under-21 striker collects a pass from his strike partner and turns Hunter easily before curling a superb effort just inches wide of the post from 20 yards out.
34 - GOAL. Rushden equalise in spectacular style against the run of play. After Dailly is penalised for a foul 20 yards out, striker Lowe steps up to fire an unstoppable left-foot free-kick that James can only wave a hand at as it arrows into the top corner of the net. West Ham United 2 Rushden & Diamonds 1.
36 - Dailly heads on to the top of the net from Noble's deep corner.
41 - Hall volleys an effort just inches over the bar from the right hand side of the Hammers' area.
Added time: 1 minute.
Half-time: West Ham United 2 Rushden & Diamonds.
Second Half:
52 - Sofiane's low cross finds Connolly who, rather than lay a pass off, again shows his hunger for goals with a neat turn and blistering shot that deflects off a defender for a corner. From the resulting kick, Ferdinand's near post header is cleared off the line by a defender.
59 - A good run from Burgess ends with the Rushden midfielder firing a left-foot shot just wide of the target.
68 - Double substitution for West Ham, Garcia replaces Sofiane and Byrne replaces Ferdinand, who is stretchered off injured.
73 - Connolly's crossfield pass finds Garcia, who cuts in from the left and fires a left-foot shot just wide of the target.
79 - GOAL! Another predatory strike from Connolly virtually assures Hammers' safe passage to the next round. Noble's corner from the left is nodded down by Dailly to Defoe, whose excellent shot on the turn is superbly saved by Turley, only for Connolly to gobble up the rebound from six yards out. West Ham United 3 Rushden & Diamonds 1.
81 - Repka booked for foul.
81 - Substitution for Rushden, Darby replaces Jack.
86 - Double substitution for Rushden, Gray replaces Mills, and Dempster replaces Hunter.
90 - Connolly's attempt to claim his hat-trick is denied by the boot of a defender as his low shot from the edge of the area is deflected just inches wide.
Added time: 3 minutes.
Full-time: West Ham United 3 Rushden & Diamonds 1.
HOW THEY LINED UP:
4-4-2
Goalkeeper: James
Defence: Ferdinand (right), Repka, Dailly, Brevett (left)
Midfield: Sofiane (right), Lee (centre, holding), Noble,
Etherington (left)
Forwards: Defoe, Connolly
Subs: Garcia (replaced Sofiane), Byrne (replaced Ferdinand,
injured)