Having secured their first trophy of the season by beating Tottenham Hotspur in Sunday’s League Cup final, Mourinho’s team strengthened their chances of delivering more silverware to Stamford Bridge.
Chelsea were helped in that aim by Manchester City’s defeat at Liverpool while they were on Wembley duty and despite the best efforts of a West Ham side determined to halt a new year slump, they ensured that advantage was not lost.
But it would have been a different story had West Ham striker Diafra Sakho made more of a succession of good chances.
And the home side were left incensed by referee Andre Marriner’s failure to punish John Terry when the Chelsea skipper blocked Cheikhou Kouyate’s late run when he was on a booking.
Ultimately, though, Chelsea’s resolve ensured they head into a week-long break having taken another step towards the title, while West Ham are still looking for their second league win since the turn of the year.
Mourinho largely stuck to his Wembley line-up as Chelsea attempted to take advantage of City’s weekend slip, making just two changes, with Thibaut Courtois replacing Petr Cech in goal and Oscar starting ahead of Willian.
That meant Kurt Zouma was offered a resounding vote of confidence by his manager, with the defender once again asked to operate in an unfamiliar midfield holding role in the absence of the suspended Nemanja Matic.
It was clear Zouma’s inexperience in front of the back four would be severely tested by a West Ham side anxious to halt their recent decline.
After Diego Costa had sent an early opportunity flying over the bar for the visitors, West Ham responded positively and threatened to go ahead before Hazard established Chelsea’s lead.
– Ramires hits post –
Enner Valencia should have done better than direct a free-kick over the bar, but it was Sakho who spurned the best chance to give the Hammers an early foothold in the game.
The Senegal forward scored seven goals in his first eight games for West Ham, but has struggled since the turn of the year and looked like a player low in confidence when he failed to turn in Kouyate’s low cross.
Those misses were made to appear even more costly when Hazard headed past Adrian in the 22nd minute to give Mourinho’s side the lead.
The move was started by the Belgian, who linked well with Cesc Fabregas before the ball was worked out to Ramires on the right.
The Brazilian whipped in a cross towards the unmarked Hazard, who directed the ball past Adrian despite suspicions of offside.
Chelsea would have doubled their lead when Hazard sent Costa clear on goal in the 35th minute, but for an outstanding saving tackle by home right-back Carl Jenkinson.
But while that undoubtedly lifted the hosts, Sakho again blew a chance to find a way past Courtois just 60 seconds later when he sent a close-range header into the arms of the fortunate goalkeeper.
It was clear from the opening 45 minutes that victory would not come easily for Chelsea.
And their task would have been considerably harder had Sakho not continued to fluff his lines, although there was little he could do about Courtois’s excellent 55th-minute save that prevented the home side levelling.
Chelsea responded in kind with Ramires striking the post after being released inside the area by the excellent Hazard and although they failed to add a second goal, their display suggested they will not give up their position at the head of the table without a fight.