Gerrard took his season's tally to 23 goals with two first-half efforts, before substitute Babel's late strike left the Reds' title hopes flickering and West Ham's Europa League ambitions dangling by a thread.
When these two sides shared a goalless draw at Anfield back in December, Liverpool went to the top of the Premier League, six points clear of third placed Manchester United with 23 matches still to play.
But now with just two games left they are level and the Reds can only hope and pray that Sir Alex Ferguson's side slip-up in their four remaining matches - starting against Manchester City on Sunday lunchtime.
With just one defeat in their last 11 matches, Liverpool had made three changes to the side that nudged Newcastle United closer to relegation last Sunday.
There was a recall for Martin Skrtel in place of the injured Xabi Alonso, while 16-goal Fernando Torres and Lucas Leiva came in for Albert Riera and Daniel Agger.
Following his side's victory at Stoke City last Saturday, Gianfranco Zola named an unchanged line-up, but results earlier in the afternoon had already meant that West Ham had slipped two places to ninth spot without even kicking a ball.
And the Hammers had still hardly kicked a ball when they found themselves trailing with just 70 seconds on the clock.
Torres telepathically sent Gerrard behind the pushed-up home defence and, as the flag stayed down, the Liverpool skipper calmly rounded the helplessly exposed Robert Green before slotting the ball into an empty net to give his side dream start.
Desperately, West Ham tried to find a foot-hold and, as the quarter-hour mark approached, Spanish striker Diego Tristan's back-header was saved at full-stretch by compatriot Jose Reina and then Radoslav Kovac nodded Mark Noble's in-swinging free-kick over the top from just six yards.
At the other end, energetic ex-Hammer Yossi Benayoun and the industrious Dirk Kuyt were looking to ensure that lively Liverpool broke at every opportunity, while the threatening Torres and Gerrard deposited long-rangers high into the stands, much to the relief of the home fans.
But seven minutes before the break, the Merseysiders doubled their lead when the retreating - and consequently booked - Luis Boa Morte was adjudged to have pulled back Torres as the pair raced for Benayoun's through pass.
Although Green brilliantly parried Gerrard's low penalty at the base of his right-hand post, the Liverpool captain reacted quickest to bundle the rebound home.
With the boos for referee Alan Wiley still ringing around Upton Park, the official merely infuriated the locals even more when he cautioned Kovac for dissent and the breaking David Di Michele for diving after the irate Italian pounced on Jamie Carragher's slip before losing his way and stumbling as he attempted to round Reina
Zola introduced youngsters Jack Collison, Freddie Sears and Josh Payne at the expense of Junior Stanislas, Di Michele and Boa Morte, while Babel and Andrea Dossena replaced Torres and Benayoun.
And seven minutes from time, Babel cemented a comfortable victory when he lashed home the rebound after he had initially headed Kuyt's cross into Green from point-blank range to start the rapid evacuation of a battered and bruised Boleyn Ground crowd.