With relegation rivals Bolton Wanderers snatching a crucial victory at doomed Sunderland to move two points clear of Glenn Roeder's team, a third straight victory would certainly have been the preferred outcome, but there were no complaints from the Hammers boss after his battling troops secured a draw on a ground that has been notably unkind to us in recent years.
Our last 15 visits to the blue half of Merseyside have provided just one victory - a 1-0 triumph in January 1994 - while the painful 5-0 defeat in last year's corresponding fixture was still fresh in the mind for the group of loyal Hammers fans who made the long trip north.
However, the recent victories over West Bromwich Albion and Tottenham Hotspur meant that Roeder's men embarked on that journey in much more confident mood, with recent rumours of illness and injury problems thankfully without substance.
In fact, Roeder was forced to make just one change to the team that saw off Spurs, as the suspended Lee Bowyer was replaced by Steve Lomas, returning from a minor injury.
Everton registered the first effort on target as early as the second minute, when Thomas Gravesen's cross from the left was met by Tomasz Radzinski, whose header was comfortably held by David James.
If the 40,158 crowd thought that would be the start of an action-packed and free-flowing affair, though, they were sadly mistaken.
With neither side willing to commit too many men forward, and seemingly incapable of stringing more than two passes together, goalmouth action was at a premium and Radzinski's header proved to be the only effort on target that either team managed to muster before the break.
Gravesen's 42nd minute booking for a cynical trip on Michael Carrick was the only other noteworthy incident in a dull and cautious first half - a style that clearly suited Roeder's men more than it did Everton in front of their impatient home fans, but with teenage sensation Wayne Rooney and veteran striker Kevin Campbell waiting on the bench for their opportunity, it seemed unlikely that Hammers would find life that comfortable for the entire 90 minutes.
Thankfully, both sides came out after the break in a more positive and attacking mood, and it was Hammers who should have taken the lead eight minutes into the half after making a bright start.
Rufus Brevett's driven pass reached Les Ferdinand, whose deft flick released Trevor Sinclair in on goal, but the revitalised midfielder saw his first time shot blocked by Richard Wright and the loose ball was cleared for a corner.
Everton boss David Moyes - celebrating one year in the hot-seat at Goodison - then acted quickly to counteract the increasing threat, making a treble substitution with 35 minutes still remaining that saw Rooney replace Brian McBride, Campbell come on for Gary Naysmith and Chinese midfielder Li Tie take the place of Scot Gemmill.
The move almost paid off immediately, as Campbell's header reached Radzinski and the Polish striker cut inside before firing in a fierce left-foot shot that was palmed away by James before Rooney's follow-up effort was blocked.
With Everton's three-pronged attack keeping Hammers on the back-foot, chances for the visitors were few and far between, but a water-tight defensive display ensured that the same went for the frustrated hosts.
Our wide pairings of Brevett and Sinclair on the left and Johnson and Lomas on the right made sure that Everton's dangerous threat from the flanks was subdued and, when the ball did find it's way into Hammers' penalty area, Tomas Repka, Ian Pearce and James were solid and commanding.
Carrick and Cole were perpetual motion in the centre of the field - denying Gravesen space in the second half and still trying their hardest to break on the counter-attack, while Ferdinand and Jermain Defoe worked tirelessly to hold the ball up and bring their team-mates into play.
Alan Stubbs almost broke the deadlock with a stretching header that sailed just inches past the post with 15 minutes remaining, and Gravesen's 30-yard piledriver brought a smart save out of James in the closing stages, but Hammers never looked in real danger of conceding.
Once again, a spirited team performance from Roeder's men and, with Sunderland to visit Upton Park next Saturday, the opportunity is in our hands to add further momentum to the battle against relegationâ€¦