As was the case last year, the world No 1 has opted not to play in any of the official grass-court tournaments in the lead up to his Wimbledon title defence but he was back in action on Thursday at The Boodles, an exhibition event at Stoke Park in Buckinghamshire.
Djokovic, denied the career Grand Slam by Stan Wawrinka in the Roland Garros final earlier in the month, looked in good touch as he edged a tight contest 6-4 6-7 (6-8) 10-8.
The Serb raced into a 5-2 lead with a double break of Gasquet’s serve and, although the Frenchman claimed one back, Djokovic managed to serve out the set.
The second set went to a tie-break in which Gasquet saved match point before taking the contest into a deciding champions’ tie-break.
Gasquet led that 7-4 but failed to close out, Djokovic claiming victory on his second match point with a forehand winner.
Djokovic is now expected to head to Wimbledon, the draw for which takes place on Friday with the tournament getting under way on Monday.