And following a bright home start, that double-strike finally sent the returning Glenn Roeder's Newcastle United, leapfrogging over Alan Pardew's men, on an afternoon when the leggy east enders gradually lost their way to goal and the West Ham boss refused to make any excuses.
Each side had enjoyed differing fortunes in Thursday evening's UEFA Cup, first round, first leg ties.
But following their slender 0-1 defeat at the hands of the Italian hit-men from Palermo, Pards made just one switch as Matthew Etherington replaced Yossi Benayoun, who found himself dropped to the bench.
Roeder, who steered his side to a 1-0 victory at Levadia Tallinn made a trio of changes as Celestine Babayaro came in for the injured Titus Bramble, while James Milner and Shola Ameobi both returned in place of Charles N'Zogbia and Antoine Sibierski.
With Carlos Tevez lining up alongside five-goal, Bobby Zamora in a more conventional 4-4-2 formation, the artful Argentinian almost drew first blood in the fifth minute when his curling 20-yard free kick crashed back off Shay Given's right-hand angle, after the fleeing Etherington had been forcefully halted in full flow.
And after Martins had wastefully drilled a low, angled shot across the face of the exposed Roy Carroll's goal, once referee Rob Styles had controversially allowed play to continue with Danny Gabbidon lying prone on the Upton Park turf, Tevez had another low, free-kick saved by the alert Newcastle 'keeper.
Earlier, a Damien Duff corner had been met by Peter Ramage's firm header, which the well-placed Carroll cradled into his ribcage and midway through the half, the Irishman's second flag kick was almost bundled home at the far post by Ameobi, who forced the Hammers' 'keeper into a brave block.
Belozoglu Emre also tested the flying Carroll from range but, in a compelling contest flowing from end-to-end, it was Newcastle old boy, Lee Bowyer, who nearly broke the deadlock in audacious fashion, ten minutes before the interval.
For when the red-faced Given's clearance fell to the Hammers' midfielder out on the right touchline, his opportunistic chip from the halfway line sailed back over his back-pedalling former team-mate, before agonisingly bouncing the wrong side of the base of the keeper's right-hand post, to keep it goalless at the break.
Tevez was replaced by Marlon Harewood for the restart and there was to be more Argentinian disappointment five minutes into the second half, when bursting from the centre-circle, the motoring Martins rode Mascherano's attempted slide-tackle and slid the ball to Duff, who fired a low, angled fifteen-yarder into the bottom left-hand corner of Carroll's net.
And midway through the half, the industrious Argentinian joined his compatriot on the bench, when Pards introduced Benayoun, while the ill Tyrone Mears was replaced by Hayden Mullins in a double-switch.
After Harewood glanced Benayoun's free-kick wide, Roeder responded by bringing on Sibierski for Ameobi and the French substitute immediately unleashed a rising 25-yarder that cleared Carroll's crossbar.
Newcastle's second goal was not too far away, though, and with just a quarter-of-an-hour remaining, Martins robbed Danny Gabbidon on the edge of the Hammers area before advancing and slotting the ball beyond the helplessly exposed Hammers' 'keeper.
But, by then, the busiest man on the pitch was referee Styles, who took the bookings count to the half-dozen mark in an ill-tempered finale that saw Given stretchered off following an accidental collision with Harewood and Roeder calmed by the match official for an over-zealous acknowledgement of the visiting fans that infuriated the West Ham supporters in a bumper, yet disappointed 34,938 crowd.