Pat's keeper Conor O'Malley had an inspired match as Derry wasted numerous chances - especially before half-time.
Against the run of play, Kurtis Byrne put Pat's ahead on 21 minutes.
Ronan Curtis levelled before half-time only for Conan Byrne to restore Pat's lead before Aaron McEneff's 84th-minute strike secured Derry a point.
Derry boss Kenny Shiels was forced to make two late changes to his starting line-up as McEneff and Mikhail Kennedy were drafted in after Nathan Boyle and Nicky Low had sustained groin injuries in the pre-match warm-up.
McEneff tested O'Malley with two great efforts as Derry made a lively start only for Pat's to take the lead on 20 minutes as Darragh Markey's through ball to Kurtis Byrne was followed by the striker stroking through Gerard Doherty's legs.
O'Malley's continuing heroics denied Harry Monaghan and the lively Ben Doherty [twice] before Curtis curled in a superb equaliser on 39 minutes.
Kennedy was then presented with a glorious chance to put Derry ahead but he failed to get full purchase on his shot as O'Malley made his ninth save of the first half.
The second half was more low key and Pat's regained the lead on 69 minutes with Conan Byrne's superb chip floating over Doherty.
To their credit, Derry kept battling away and McEneff blasted in a second equaliser from the edge of the box six minutes from time after being set up by Conor McDermott.
Derry remain without a victory since the 4-0 win over Drogheda United on 18 March, which was the day before the sudden death of club captain Ryan McBride.
Derry City's winless run was extended to seven games as they drew 2-2 against St Patrick's Athletic in Friday's Premier Division game in Buncrana.