Cameroon striker Eto'o, whose age was questioned recently in unguarded comments made by Mourinho, celebrates his 33rd birthday on Monday and stood crooked at the corner flag, as if using it as an old man's stick, following his goal.
Demba Ba, another much-derided Chelsea striker, then scored twice in his late cameo after replacing Eto'o.
The victory extended Mourinho's unbeaten Premier League home record to 75 games and took Chelsea seven points clear of Arsenal and Liverpool and nine ahead of Manchester City, the Portuguese's title favourites.
Cardiff captain Steven Caulker led from the front with two goals as the Welsh club won a crucial encounter against fellow strugglers Fulham 3-1.
The centre-back scored in either half to give the Bluebirds' battle against relegation a boost while increasing the woes of their bottom-of-the-table opponents.
Cardiff manager Ole Gunnar Solksjaer had said in the build-up the match was one they must win and in doing so he registered only his second league victory in nine matches since taking the job in January.
Caulker put them ahead on the stroke of half-time when he converted Craig Noone's deflected cross but early in the second half Giorgios Karagounis' corner was flicked on by John Heitinga for Lewis Holtby to convert his first goal since joining on loan from Spurs in January.
They were level for eight minutes before Caulker headed Cardiff back in front and when goalkeeper Maarten Stekelenburg's saved Jordon Mutch's header only for the rebound to go in off his own defender Sascha Riether.
Victory put them within a point of safety with West Brom, who lost 3-0 at home to Manchester United, the team immediately in their sights.
United kept alive their slim hopes of a top-four finish after Phil Jones put them ahead 10 minutes before half-time with a header.
After the break Wayne Rooney nodded in the second before substitute Danny Welbeck added a late third.
United, however, still remain nine points adrift of Manchester City, who currently occupy fourth spot but have two matches in hand over their neighbours.
Norwich edged four points clear of the relegation zone with a 1-1 draw at home to Stoke, who had goalscorer Jon Walters sent off five minutes after scoring the equaliser.
Bradley Johnson's header from Robert Snodgrass' 56th-minute free-kick put the hosts ahead only for Sebastien Bassong to foul John Guidetti to allow Walters to score from the spot in successive weeks.
However, the goalscorer was sent off for clattering into Alex Tettey as the Potters saw out the final 13 minutes with 10 men.
Southampton consolidated their position in ninth place as Jay Rodriguez's breakaway in the 37th minute provided the only goal against Crystal Palace, who themselves are only two points above the bottom three.