Robin van Persie snatched a dramatic stoppage time equaliser to earn Manchester United F.C. a deserved share of the spoils after Didier Drogba, starting for the injured Diego Costa, headed the visitors in front in the 53rd minute from a corner.
Chelsea seemed likely to hold out but just before the final whistle Branislav Ivanovic was sent off for a second yellow card and from the free kick Thibaut Courtois saved from Marouane Fellaini but could not keep out Van Persie's fierce follow-up.
The draw extended Chelsea's lead to four points over second-placed Southampton and six over champions Manchester City but they would have been expected to see the game out after a strong second-half performance.
It was only the second time this season Mourinho's side have failed to take all three points, both games being in Manchester, where they also drew 1-1 with City.
Mourinho summed up the game as "a good Manchester United but a very good Chelsea.
"My feeling is that we had a good first half and a fantastic second half," he said.
A relieved-looking Van Gaal said United's point was deserved.
"We have created a lot of chances, much more than Chelsea," he said.
After the 36-year-old Drogba's goal, Chelsea appeared in charge, and Willian and Ivanovic had chances to extend their lead.
United fought back but were repeatedly frustrated.
Van Persie fired one shot at point-blank range into Nemanja Matic's stomach, flattening the midfielder, and had another low left-footer saved at the near-post by Courtois.
Chelsea's Eden Hazard posed a continuous threat as he picked holes in the United defence.
For the home team, another Belgium international, Adnan Januzaj, looked dangerous down the wing and fired stinging shots narrowly off target in both halves. Van Persie also came close with a shot and a back-header in the first period.
Seven wins and two draws from nine games leave Chelsea in an enviable position. United, meanwhile, having briefly reached fourth place, find themselves back in eighth after a second successive draw.
The consolation for them is having equalised right at the end again, just as they did in a 2-2 draw at West Bromwich Albion last Monday.
Van Persie believes they are steadily improving. "We can be happy with a point," he told Sky Sports. "It's getting better every single day. It's still early doors and we can catch Chelsea, yes."
A year ago Mourinho had been criticised for Chelsea's negative approach at Old Trafford when he played without a recognised striker and achieved a goalless draw.
Without Costa and fellow striker Loic Remy, there might have been a temptation to adopt the same tactics but starting with Drogba in front of Willian, Oscar and Eden Hazard reflected their confidence after an impressive start to the season.
Mourinho was reluctant to be drawn on Ivanovic's two yellow cards for fouls on Angel Di Maria but was clearly not happy about the dismissal.
Van Gaal, however, said: "I've seen it on television and he touched him two times."
United's manager added that what pleased him most was the way his side kept going, saying: "We showed again that we believe until the end in making a goal."
They face a tough assignment next, in the Manchester derby away to City next Sunday.