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Davenport drew Gary McAllister's side level 16 minutes into the second-half, seizing on a defensive blunder from Portsmouth defender Linvoy Primus before firing home from four yards out.
Portsmouth striker Vincent Pericard scored his fourth in four games to give table toppers Pompey a 50th minute lead.
The on-loan Juventus forward brilliantly chipped Coventry goalkeeper Fabien Debec from the edge of the area after racing on to captain Paul Merson's majestic cross field pass.
Coventry had had the better of an uninspiring first half and were unlucky not to go in leading at half time.
Player-manager McAllister set the tone for a pulsating afternoon at Fratton Park when he forced a fine save from Hislop from a 25 yard free kick after just two minutes.
Loan striker Lee Mills was unlucky not to put Coventry ahead when his 20 yard shot cannoned off the Portsmouth cross bar on the stroke of half-time.
Both sides had chances to win the game late on and Pompey had Hislop to thank for keeping their home record in tact 10 minutes from time when he brilliantly tipped midfielder Ritchie Partridge's close-range header over the crossbar.
Coventry boss McAllister said: "I thought we were unlucky not to win the game and their is a tinge of disappointment in the dressing room.
"But we would have taken a point before the game though I can't be too disappointed."