The Brazilian opened the scoring after just 11 minutes when he latched on to a long ball from Juan Mata and fired past Pepe Reina.
Drogba scored Chelsea’s second just after the break, becoming the first player to score in four FA Cup finals.
Andy Carroll fired Liverpool back into the contest with a fine finish just eight minutes after coming on as a substitute.
The £35 million striker thought he had levelled matters with less than 10 minutes remaining but his header was adjudged not to have crossed the line as Chelsea’s keeper Petr Cech displayed some brilliant reflexes by deflecting his header on to the bar. Carroll turned away to lead Liverpool’s insistent protests that the ball had crossed the line but referee Phil Dowd and assistant referee Andrew Garratt waved play on, with even a succession of replays proving inconclusive.
Chelsea survived and can now turn their attentions to the Champions League final against Bayern Munich in Germany later this month as they face an increasingly arduous task to finish in the Premier League’s top four.
As Di Matteo celebrated and captain John Terry raised the trophy, the Italian increased his claims to become the permanent successor to Andre Villas-Boas by landing a trophy.
For Liverpool, their season will now be regarded as a relative disappointment after failure to add the FA Cup to the Carling Cup and not mounting a challenge to reach the Champions League places.
The final started with £85m worth of striking talent on the bench as Carroll was a Liverpool substitute and Chelsea’s Fernando Torres missed out on a starting place against his former club.
The Reds were on the back foot early on when a catalogue of defensive errors led to Ramires giving Chelsea the lead. Jay Spearing conceded possession in midfield and Ramires escaped Jose Enrique far too easily before scoring at the near post with a shot Reina should have saved