The setback left the Blues just one point clear of rivals Manchester United at the top of the Premier League.
But if Chelsea win their remaining three games, two at home to Stoke and Wigan with a trip to Liverpool sandwiched in between, the Blues will be champions for the first time since 2006.
Captain John Terry was dismissed for two bookable offences as Spurs delivered a real blow to Chelsea's hopes of keeping their previous four-point lead in tact.
He will miss their next home game against Stoke on Sunday by which time Manchester United could have regained the leadership.
But while Chelsea can cope with Terry's absence now that Branislav Ivanovic is fit again, they may have to rely on winning the next three games with talismanic Drogba still nursing his groin problem.
Drogba has scored 32 goals this season but has struggled since it was made clear the Ivorian is battling an injury.
The striker tweaked the groin at the start of the second-half against Tottenham and wanted to come off but Chelsea coach Carlo Ancelotti had already made three changes - two of them at the interval.
Drogba had to play on through the pain barrier for the remainder of the second-half but looked a pale shadow of the striker who has once again terrorised defences in the top flight this season.
He is unlikely to want to carry the injury into the World Cup finals in South Africa this summer and is almost certain to undergo surgery. But the big dilemma facing the club and the player is when will that be carried out.
"It's his decision," said Ancelotti. "He doesn't have a big problem. It's more about controlling the situation.
"He'll take a decision at the end of the season, whether he has surgery or not. But it's not sure he'll have surgery."
Chelsea will continue to monitor Drogba's injury but, against Spurs, he was certainly far from the marauding figure that has been on display for much of the season.
Nicolas Anelka, who scored the winner from a Drogba cross against Bolton last week, may now get the chance to spearhead their bid for the title along with his Ivorian team-mate Salomon Kalou.
Kalou insists that Drogba remains one of the best strikers in the game and their close relationship could reap dividends for the Blues on the run-in.
"Every time I have the chance to work with him I listen to what he has to say - he is very important to me," said Kalou.
"When you're talking about strikers in the game today, Didier is one of the best and I want to take advantage of this opportunity to learn from him.
"Didier is like a big brother to me. First of all we come from the same country and that makes us closer.
"He still takes me to one side at training and gives me tips. We are always working in front of the goal. He is always so sharp in front of the net and I want to improve that side of my game.
"I can improve and develop every season by playing with him. Didier this year has been very important for the club, like every year.
"He has an amazing goal-scoring record for Chelsea and as a player it is a level I want to reach. I'm taking it step by step but I am trying to get in the team regularly first."