Carlo Ancelotti's side stay six points behind Manchester United, while Avram Grant's charges are rock bottom of the Premier League
And so it finally came. After 734 minutes, Fernando Torres scored his first goal for Chelsea since his £50 million arrival from Liverpool in January, keeping Carlo Ancelotti's side in the running with league leaders Manchester United.
Ancelotti had previously insisted Torres would score Chelsea's important goals before the end of the current campaign, and in the context of this game, where West Ham threatened to spark a revival after going behind to a Frank Lampard strike before the interval, the Spaniard's strike, eight minutes after coming on as a substitute, killed off any hopes of a comeback from Avram Grant's charges.
The win, which was sealed by Florent Malouda in the closing stages, keeps Chelsea six points behind Manchester United, and extends their lead over third-placed Arsenal to three points, although Arsene Wenger's side travel to Bolton on Sunday.
For West Ham, defeat leaves them bottom of the Premier League, two points adrift of safety, and in a month where Grant oversaw four straight defeats, his side now have four games remaining to secure their survival.
Both sides had big name players unavailable for the clash with Alex and Ramires out for Chelsea, West Ham were without the services of newly-crowned Football Writers' Player of the Year, Scott Parker.
Chances, along with the torrential weather, rained down on both goals but neither side could find the accuracy required to open the scoring. Both Malouda and Salomon Kalou broke the West Ham defence open, but in the case of Malouda, when one-on-one with Robert Green, he should have chipped the ball over the advancing goalkeeper instead of trying to place it low.
Much of the action in the first period was played in the visitors' half and stout defending was the order of the day for Grant's men. West Ham stuck to their plan, however, and threatened with a number of counter attacks. The best coming from Demba Ba's strike which stung the palms of Petr Cech.
Moments later, West Ham had their best chance to open the scoring when a powerful and swift run from Freddie Sears down West Ham's left opened an avenue which allowed him to cross deep to the far post where a diving Jonathan Spector couldn’t direct his header beyond Cech.
As the thunderstorm over west London settled directly above Stamford Bridge causing various floodlights and advertising boards to go out, pressure from the hosts finally told as Lampard opened the scoring. After excellent forward play and from Ashley Cole, the left-back's squared pass across the box was met by the midfielder, who smashed the ball past Green.
As the weather continued to soak Stamford Bridge, Chelsea were looking more and more comfortable and in control but Ancelotti’s hand was forced when Michael Essien, who pulled up in the first half, left the field injured to be replaced by Yossi Benayoun.
The injuries continued as West Ham’s Mark Noble was stretchered from the field and replaced by Robbie Keane, who was welcomed with a round of boos from the Chelsea following.
After the restart, both sides continued to press for a goal and the chances were still not been taking, but in the case of David Luiz, who hammered a long-range effort off the crossbar, it wasn't for the want of trying.
West Ham's creativity was producing opportunities but the end product was a reminder as to why they have struggled this season. Ba and Keane both squandered chances which should have easily given Cech problems.
And then came Torres to kill off the tie. Entering the game once again as a substitute for the in-form Didier Drogba, the Spaniard showed a flash of his old self as he turned sharply in the box and lashed his left-footed effort past Green.
Malouda sealed the tie moments before the final whistle with a crashing drive to keep Chelsea in with a chance of retaining their Premier League crown. While West Ham suffer no respite, as they take on Manchester City in their next outing.