After a goalless first half, a horror mistake by Saints defender Steven Anderson when he allowed himself to be dispossessed by Kris Commons let Anthony Stokes fire the visitors ahead.
To the anger of the Saints players and fans, skipper Dave Mackay was shown a straight red card in the 75th minute by referee John Beaton for a foul on Hoops substitute Derk Boerrigter inside the box - with Nir Biton converting from the spot-kick as the Perth claims of a dive by the Dutchman continued.
Hoops midfielder Callum McGregor added a third in the 85th minute with a low drive which goalkeeper Alan Mannus should have saved, to compound a miserable night for the Scottish Cup winners.
Partick ensured there would be no repeat of last season's problems at home as they notched an emphatic 4-0 win over Ross County in their opening game of the campaign.
Thistle had been forced to wait until a 3-1 triumph over Aberdeen in February to secure their first league victory at Firhill last term.
But they got off to a flier this time thanks to strikes from Stuart Bannigan, Gary Fraser and Stephen O'Donnell, and a debut own goal by Ben Frempah.
Bilate struck in the 82th minute, meaning Jackie McNamara's side earned a deserved 1-0 win after they had done most of the pressing in the second half.
Kilmarnock suffered defeat in the first match on their artificial pitch as goals from Peter Pawlett and Ryan Jack handed Aberdeen a 2-0 victory, while a strike from Ali Crawford and an unlucky own goal conceded by Marc McAusland earned new boys Hamilton a deserved 2-0 win at St. Mirren.
Elsewhere, Inverness and Dundee played out a stalemate in the Highlands.