For José Mourinho and Chelsea, there was beauty in this East End stroll. Needing victory after the loss at Newcastle United and the fortunate home draw against West Bromwich Albion, they found opponents only too happy to oblige.

West Ham United were a shambles in the first half. Sam Allardyce persisted with his 4-6-0 formation and the manager watched his players offer nothing and, seemingly, look to do little more than cling on.

So bad were his tactics and his team that he made two substitutions in the 40th minute, with one of the new faces being a striker, Modibo Maïga. Joe Cole was furious to be withdrawn and he stormed straight off to the dressing room.

The damage was done by then. Chelsea took advantage of West Ham's lack of ambition and, also, defensive slackness; the opening goal, thrashed home from the penalty spot by Frank Lampard against his old club, followed a faintly ludicrous lapse. Oscar got the goal that his man-of-the-match performance deserved after the half-hour and that was pretty much that.

Mourinho's team were helped on their way but they were stable, confident and incisive. They might have struggled at times when opposing teams have flooded the midfield but not here. Mourinho's only gripe was that the third goal took so long to come and, at 2-0, Chelsea risked allowing West Ham back.

Maïga did fluff their only chance on 65 minutes, and it was a glorious one, but a comeback never looked likely. Lampard scored again, shooting home after yet another flowing move and West Ham, despite showing more spirit and purpose in the second-half, could not escape being booed off.

Allardyce believes that the striker-less strategy is the best way to compensate for the absence of Andy Carroll and it did work in the 3-0 win at Tottenham Hotspur on 6 October. Since then, though, there have been two points taken and the club have been left to teeter above the relegation places.

The tactic, quite simply, feels negative at home and when any manager tears up a blueprint after 40 minutes, it is tantamount to an admission that he got things horribly wrong in the first place.

What Allardyce did not need was the darkly comic moment that served to put Chelsea in charge. Gary Cahill's chip did not appear to present a problem but Guy Demel contrived to create a big one, when his attempt to get the ball back to Jussi Jaaskelainen with his thigh went askew. Oscar nipped in, Jaaskelainen sent him spinning and the only discussion concerned the colour of the goalkeeper's card.

Mourinho said it should have been red; the referee Chris Foy ruled that it was not even yellow. Oscar was running away from goal and it was not a clear scoring opportunity. Lampard relished converting in front of the Bobby Moore stand and the supporters who continue to jeer him.

Chelsea ratcheted up the intensity, Lampard twice went close and Oscar's goal came as no surprise. It was another soft concession. James Collins lost his bearings after Eden Hazard's flick and Oscar ran and kept running before, in the absence of any challenge, he threaded low into the corner from the edge of the area.

Allardyce chuntered about Cole's reaction to his removal. "All any player ever does is think about himself," Allardyce said. "It's up to him the next time he gets a chance to make it impossible for me to substitute him."

Allardyce also removed his captain, Kevin Nolan, in the 76th minute, a decision that was greeted by cheers from the home crowd.

Chelsea might have had more before the interval – Jaaskelainen made one save from Samuel Eto'o – and the visitors could revel in lovely individual flickers, with Hazard running Oscar close for star billing. Eto'o showed his touch and skill.

Mourinho had started Mikel John Obi in front of the back four to counter West Ham's high balls and allow Lampard to get forward while the team was configured to allow Hazard to eschew any defending. He enjoyed himself and so did the travelling fans. "Frankie Lampard," they told their West Ham counterparts. "He's won more than you."

Chelsea pushed for more. Cahill had a header cleared off the line by Mark Noble and Oscar was off target following a Chelsea counter. Maïga's point-blank miss, after Demel's wonderful run and cross, seemed to sum things up for West Ham and Lampard twisted the knife with his second.

Mourinho said that a "third game without a win would not have been acceptable" but for Allardyce, comfort was scarce. "We've lost our home fortress," he said. "We are struggling in front of goal and now, we are suffering with our defensive errors."