Ben Doherty opened the scoring on 18 minutes after a superb Derry break, sprint up the pitch to strike with his left foot past Rovers keeper Alan Mannus .
Johnny Kenny scored his first league goal on 26 minutes before McGonigle’s winner eight minutes after half-time.
The result between last season’s champions and runners-up ended the home side’s 29 game unbeaten home run.
Doherty’s goal came as he ran on to a Will Patching’s through ball, with the midfielder showing great composure to fire into the bottom right-hand corner after he had outpaced the Rovers defence.
Kenny levelled in the 26th minute after a Sadou Diallo’s pass was intercepted by Gary O’Neill who was then fouled.
As the referee played the advantage Markus Poom pressed forward, passing to Kenny, with his close-range strike beating Brian Maher.
Good build-up play down the wing by Patching helped to restore Derry’s advantage in the 53rd minute as Ryan Graydon’s cut back then found McGonigle who swept the ball to the net.
The result was the Candystripes’ first victory at Tallaght Stadium since 2017.
In contrast, the defending champions continue to search for their first league win of the season as their unbeaten home league run since mid-2021 came to an end.
Rovers had the stronger first half and Derry’s opening goal came against the run of play.
Dylan Watt had the first chance of the match as his volley from the edge of the box was off target before Derry midfielder Patrick McEleney brilliant blocked Graham Burke’s point-blank strike.
Derry keeper Maher twice saved Trevor Clarke shots with Burke blasting the rebound wide on the second occasion.
However, Ruaidhri Higgins’ men then came more into the game as Rovers keeper Alan Mannus had to stretch to push away a Patrick McEleney 25-yard effort.
After McGonigle restored Derry’s lead, Rovers created multiple chances later on, with the closest they came as Candystripes substitute Ronan Boyce cleared off the line following a goalmouth scramble.
Next up for Derry is an away to UCD on Monday, March 6.
Shamrock Rovers: Alan Mannus; Trevor Clarke, Sean Gannon, Sean Kavanagh (Sean Hoare 80), Gary O’Neill, Neil Farrugia, Markus Poom, Dylan Watts (Liam Burt 80), Jack Byrne, Graham Burke (Simon Power 74), Johnny Kenny (Rory Gaffney 74).
Derry City: Brian Maher, Ciaran Coll, Mark Connolly, Shane McEleney, Ben Doherty, Sadou Diallo (Jordan McEneff, 78), Will Patching, Patrick McEleney, Ryan Graydon (Cian Kavanagh 86), Ollie O’Neill (Brandon Kavanagh 80), Jamie McGonigle (Ronan Boyce 80).
Referee: Neil Doyle.
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