Thompson opened the scoring with a first-half header, before Conor Newton gave the away side a two-goal cushion.
Thompson then grabbed his second of the day with a cool finish for his boyhood club to give St Mirren a much-needed victory.
The home side had the game's first opportunity when James Craigen's shot from distance went narrowly wide to the relief of St Mirren goalkeeper Marian Kello.
Gabriel Rojo de la Vega should have given Thistle the lead after six minutes but was unable to find the target with a close-range header from a corner.
The visitors had the first shot on target in the 15th minute of the game with an effort from outside the box from Kenny McLean which was put out for a corner by Partick goalkeeper Scott Fox.
McLean took the resulting corner which was headed into the left-hand corner of the net by Thompson from six yards to give St Mirren an early lead.
Partick tried to hit back before half-time with Kris Doolan and Steven Lawless both forcing saves from Kello as the visitors clung to their lead.
The lively McLean fired over shortly after the break before the home side forced a succession of corners without managing to trouble Kello.
Stephen O'Donnell had an effort blocked for the home side just shy of the hour mark, but he would ultimately have a decisive impact on the game.
Already on a booking following a first-half challenge on John McGinn, O'Donnell made a badly-timed challenge on the same player forcing referee John Beaton to send him off for a second bookable offence after 69 minutes.
Things went from bad to worse for the home side when Newton doubled the visitors' lead after 71 minutes.
Newton latched onto a pass from Paul McGowan on the right side of the area before rifling the ball across Fox and into the bottom left corner of the net.
The 10 men valiantly tried to get back into the contest but Kallum Higginbotham was unable to trouble Kello with two efforts from range.
But the visitors were not finished. Daniel Grainger slipped the ball to Thompson in injury-time and the forward made no mistake firing past the hapless Fox as St Mirren made it three to claim all three points.
The result moves St Mirren up two places to ninth in the Scottish Premiership.