In an intense, nervy, sometimes frantic tussle, Liverpool scored first, Sami Hyypia flicking home a header from a Danny Murphy free kick 30 metres out on 11 minutes after Desailly had brought down striker Milan Baros.
But the stunned home fans had less than three minutes to wait for the equaliser, Danish winger Gronkjaer sending a pinpoint cross for Desailly to head home from close range.
It was the Flying Dane who scored Chelsea's second in the 27th minute with a low left-foot shot from just inside the area that he squeezed into the bottom corner of Jerzy Dudek's goal.
The teams were level on points before Sunday's match, but Chelsea's superior goal difference meant they needed only a draw to clinch fourth place and a spot in next season's Champions League qualifying competition.
Both Chelsea's Italian coach Claudio Ranieri and Liverpool's French boss Gerard Houllier had likened the match to a cup final with up to £15 million ($24.06 million) at stake for a place in the Champions League.
"I don't think we lost the Champions League here today," Houllier said afterwards. "We lost it ... when we went so many games without a win in mid-season."
With a persistent drizzle making the ball slippery, Chelsea had a lucky escape in the 77th minute when goalkeeper Carlo Cudicini dropped the ball and Baros bundled it into the net. But the ball had bounced off the Czech striker's hand and the goal was disallowed.
As tempers frayed in fast-and-furious end-to-end action in the dying minutes, Gerrard was sent off for a flying tackle on Graeme Le Saux.
It was Chelsea who finished stronger, topscorer Gianfranco Zola, who has yet to decide whether to stay for a seventh season, coming on as substitute and weaving magic through the Liverpool defence.
"I hope he stays," Ranieri said afterwards. "He is so important for us. Look at the last 20 minutes how he played."
The diminutive Zola, 36, a favourite with the fans, led Chelsea on a noisy lap of honour after the game.
"This group [of players] is very important to Chelsea," Ranieri said, adding that he felt the secret of the side's success this season had been continuity.
Houllier also indicated that he would be making few changes next season. "We have a good team," he said. "It's still young and I don't think we need a lot of players. Sometimes you need a bit of stability."
