Doolan ran riot with two goals either side of half-time, Nathan Eccleston adding an 89th-minute fifth to give Thistle a first victory of 2015 and leave the Accies without a point in three games since their manager left for Norwich.
Neil will be joined at Carrow Road by assistant Frankie McAvoy after this weekend, leaving Martin Canning to fend for himself in his role as caretaker player-manager, and Hamilton will begin life without their long-serving coach five points off third place.
Thistle were well worth their first home win in the league since November 8, dealing comfortably with opponents who came into the game with as many league goals as champions Celtic.
Ali Crawford did miss a couple of presentable early opportunities, but Partick were ahead when Doolan applied the finishing touch to Ryan Stevenson’s goalbound lob a minute before the half-hour.
Steven Lawless fired wide before Doolan’s second (44), buried after a smart turn, and Lawless hit the bar soon after half-time as Partick continued to dominate.
Their reward came in extravagant style courtesy of a back-heeled hat-trick goal from Doolan (60), who completed his personal haul two minutes later with a header from Stephen O’Donnell’s cross.
Doolan made way for Eccleston, and it was the substitute who followed up his own saved shot to finish the scoring.