United had to at least draw to keep the title race mathematically alive but were stunned at Old Trafford when Jay Rodriguez headed home after the break.
Pep Guardiola says winning the Premier League will be one of the greatest achievements of his glittering career after Manchester City moved to the brink of the title with a stylish 3-1 win over Tottenham.
Aguero had been out for a month prior to last week's Manchester derby, in which he emerged from the bench and appeared to be fouled by Manchester United's Ashley Young late on - only for referee Martin Atkinson to wave away penalty appeals. You didn't expect City to beat the Invincibles, did you? After, we wait for the results of United but, if it does not depend on the results of United, it is in our hands.
And that was also the case on Sunday, as United failed to spark the imagination in any tangible way even though they were playing a side that had hadn't won in the league since January.
A week after City surrendered a 2-0 lead to lose 3-2 to United and squander the chance to wrap up the title in ideal style against their arch-rivals, it was relegation-bound West Brom who served it up on a plate.
Jake Livermore had one decent effort saved by David De Gea and Lukaku smashed an effort right into Ben Foster's face but that was about it.
Prompted by the abject nature of the opening 45 minutes, Mourinho brought on Jesse Lingard at half-time and he was immediately in the heart of the action as United attempted to wake from their slumber.
City will be crowned champions if Manchester United slip up against West Bromwich Albion or Bournemouth in their next two matches.
The second half was not much better but Foster did wonderfully well after 66 minutes to tip a Lukaku effort around the post before the visitors resistance was then unexpectedly rewarded with 17 minutes remaining.
"West Brom is a club I care about a lot", he said.
"Our Time. Our City".
"You win titles with consistency at every level, not just the performance level but the mental level and the day by day".
Chelsea were undefeated at home in the 2004/05 season, winning 15, drawing four and conceding just six goals.
The France worldwide scored two goals - the first time he has done so in the Premier League - in a remarkable second-half recovery from United as they won the Manchester derby 3-2 to deny City a win that would have seen Pep Guardiola's men clinch the title.