Both clubs are now level on 81 points with two games remaining. However, United have a better goal difference which makes them favourites to retain their title.
Within seconds of the start of the must-win game for the home side, United's Wes Brown mistimed a back header to Edwin Van der Sar. The Dutchman failed to hold the ball and Joe Cole zipped into the box. He passed to Salomon Kalou whose drive into the United area was snuffed out.
Seconds later, Michael Essien saw a left-footer from the edge of the box expertly collected by the United goalkeeper.
Nemanja Vidic collided with Didier Drogba's knee on 13 minutes and had to be carried off and replaced by Owen Hargreaves.
United's first attack on 15 minutes saw a long run and shot by Nani sail high over Petr Cech's crossbar when a pass to Ryan Giggs, free on the right would have been a better option.
On 20 minutes a run by Joe Cole into the United area seemingly fizzled out. However, the ball rebounded to the England midfielder who rattled the angle of upright and crossbar with a fierce right-footed drive.
With the fourth official showing four minutes of stoppage time left in the first half, Drogba angled the perfect cross to the far post and Ballack, who had ghosted in unmarked, headed the ball from six yards back across the path of Van der Sar and into the far corner of the net.
Chelsea started the second half as they finished the first, pressing United back. The consequence saw Brown booked on 52 minutes for a cynical foul on Essien.
But calamity struck for Chelsea five minutes later when Ricardo Carvalho gifted the ball to Rooney 30 yards out.
The England striker raced towards the edge of the Chelsea area and, with John Terry baring down on him struck a low, right-footer past the despairing dive of Cech as the ball bounced off the upright and into the net for an unlikely equaliser.
Sir Alex Ferguson, sensing a victory might now be possible, introduced Cristiano Ronaldo to the fray on 62 minutes for Rooney but not before Ryan Giggs had flashed in a left footer which Cech did well to parry away.
Chelsea boss Avram Grant brought on Nicolas Anelka in the 66th minute for Paulo Ferreira.
Six minutes later Chelsea almost restored their lead when Van der Sar produced a breathtaking save from a Drogba free-kick.
Ronaldo produced a trademark free-kick of his own three minutes later but Cech was equal to it.
Grant's last throw of the dice to win the game and retain a title bid came through the introduction of Andriy Shevchenko on 81 minutes for Kalou.
With five minutes remaining Essien whipped in a byline cross, Michael Carrick handled the ball and a penalty was awarded.
Van der Sar was booked for time-wasting, but up stepped Ballack to blast the ball home and restore Chelsea's lead.
Chelsea still had to clear the ball off the line when Ashley Cole was in the right place to keep Ronaldo's left-footer out.
And even Shevchenko hacked the ball off the goal-line from Darren Fletcher's header deep into stoppage time.
But Chelsea hung on and the title race goes on for another week.