Portsmouth 1 Fulham 1
Pompey were rocked by the pre-match departure of Redknapp to replace Juande Ramos at Tottenham in the early hours of Sunday morning.
The South Coast side looked to be heading for an against the odds win when Peter Crouch finished neatly in the 61st minute, but Dempsey caught the home defence napping three minutes from time to sidefoot home from fellow substitute Erik Nevland's cross.
Stand-in manager Tony Adams was given a rapturous welcome form the Portsmouth fans in the build-up to kick-off and his newly inherited side could have been in front twice in the space of a few seconds in the ninth minute.
First, defender Younes Kaboul saw his header from a Lassana Diarra corner cleared off the line by Paul Konchesky.
Papa Bouba Diop should have made certain when Kaboul fizzed in a low cross from the rebound, but the Senegal international blazed over.
David James almost gifted Fulham the lead three minutes later when he fumbled Simon Davies' attempted cross, but got back in the nick of time to stop the ball crossing the line.
Nadir Belhadj lifted the gloom around Fratton Park with a mazy 31st minute run, beating three Fulham defenders, and was only denied his first Premier League goal by Mark Schwarzer's fine save with his legs.
Former England midfielder Danny Murphy showed he is still a class act, with a thunderous volley which sailed just wide on the stroke of half-time.
Jermain Defoe wasted three good chances in the opening nine minutes of the second half, before passing for Crouch to finish low into the bottom right-hand corner of the net just after the hour mark.
Algerian Belhadj was unlucky not to extend Pompey's lead 21 minutes from time when he fired a left-foot shot against the post.
But it was Fulham who had the last word through American international forward Dempsey, who silenced the home fans with time running out at Fratton Park.