Jose Mourinho’s side would have moved eight points clear of second placed Manchester City if they had beaten Southampton, but instead they had to settle for a share of the spoils in west London.
Yet Chelsea failed to press home their advantage and Southampton equalised eight minutes later when Dusan Tadic converted a penalty awarded for a Nemanja Matic foul on Sadio Mane.
The Blues laid seige to the Southampton goal in the closing stages, but Oscar, Juan Cuadrado and John Terry all wasted chances to seal a victory that would have left them well on course to win the English title for the first time since 2010.
The frustrating result came just days after Chelsea crashed out of the Champions League on away goals following a 2-2 draw against Paris Saint Germain in front of their own supporters.
Chelsea have now drawn their last three home matches in all competitions, but Mourinho was still relatively happy to see his side move six points clear of City, who were surprisingly beaten by struggling Burnley on Saturday.
“I agree Chelsea not winning at home is not a good result,” he said.
“But yesterday we had five points more than City, now we have six points more and one fewer match to play.
“It makes our situation better than before the game. It’s positive rather than negative.”
At Old Trafford, Rooney was firmly in the spotlight as fourth placed United produced a rare heavyweight display in a spluttering campaign to move within one point of third placed Arsenal.
Louis van Gaal’s side made the perfect start as they took the lead in the ninth minute when Marouane Fellaini, played in by Michael Carrick’s fine pass, kept his composure to beat Tottenham goalkeeper Hugo Lloris with a low left-footed shot.
Carrick went from provider to scorer 10 minutes later when United’s former Tottenham midfielder looped a header past Lloris after Fellaini’s initial effort had only been half cleared.
It was Carrick’s first goal since February 2014, but Rooney ensured the match would be remembered mostly for his contribution in the 34th minute.
Earlier on Sunday, video footage emerged of Rooney being knocked out by Stoke defender Phil Bardsley during a supposedly friendly sparring session, with both men wearing boxing gloves, in the England striker’s kitchen last month.
And Rooney seized the opportunity to poke fun at himself after he rampaged through the Tottenham defence to fire home following Nabil Bentaleb’s mistake.
With all eyes on him, Rooney celebrated by miming a series of punches and then falling onto his back as if knocked out.
Asked about Rooney’s boxing antics, a less than amused van Gaal launched a scathing attack on the media coverage.
“In what a world we live that we are talking about such a thing – that a newspaper paid a lot for a video and I am answering questions about that,” he said.
“What is this world, twisted? I don’t want to answer questions about such things.”
Elsewhere, Everton eased their relegation fears with a 3-0 stroll against Newcastle at Goodison Park.
Roberto Martinez’s team started the day only three points above the bottom three, but they went in front after 20 minutes when Republic of Ireland midfielder James McCarthy scored his first goal of the season with a 20-yard drive that deceived Newcastle goalkeeper Tim Krul.
Everton were on course to end a run of five league games without a win by the 56th minute when Belgian striker Romelu Lukaku drove home a penalty after Newcastle’s Yoan Gouffran brought down Aaron Lennon.
Newcastle’s forgettable afternoon got even worse moments later when defender Fabricio Coloccini was shown a straight red card for fouling Lennon and Ross Barkley netted the third goal in stoppage-time.
On Monday, fifth placed Liverpool, five points behind Manchester United, will look to bolster their challenge for a top four finish when they travel to Swansea.