Strikes from Conrad Balatoni and a double from Lyle Taylor sunk the visitors after a goalless first half in which Barry Robson saw his penalty saved.
Six minutes in and the hosts were the first side to produce a shot but Gary Fraser's low effort did not cause much trouble to Dons goalkeeper Jamie Langfield.
Ten minutes later and the visitors were awarded a spot-kick after Partick keeper Paul Gallacher brought down Adam Rooney, leaving referee Alan Muir no option but to point to the spot and caution the Thistle number one.
However Gallacher was to make amends for his reckless challenge when he dived low to his right to stop Robson's penalty, with Andrew Considine firing the resulting rebound past the post.
Seven minutes later and Aberdeen had a soft claim for their second penalty following another collision between Rooney and Gallacher.
For the majority of the first half the match was peppered with needless fouls as Aberdeen's more physical approach brought about a number of stoppages.
With 32 minutes on the clock Aberdeen skipper Russell Anderson produced a superb block to deny Prince Buaben from opening the scoring for the the Firhill side.
Three minutes later and Rooney, a constant thorn to the Thistle backline all afternoon, was denied by Gallacher - who touched aside his downward header.
The deadlock should have been broken in the 42nd minute when, following a period of sustained pressure, the hosts broke away on a counter-attack but Lyle Taylor fired a poor effort wide of Langfield's right hand post when a pass to the unmarked Chris Erskine appeared to be the better option.
One minute into the second half and Joe Shaughnessy got on the end of a Jonny Hayes cross but his headed attempt went wide.
Five minutes later and Kallum Higginbotham tested Langfield with a powerful 18-yard effort which the Dons stopper did well to parry away.
Thistle started the second half with a real urgency and Bauben was next to have an attempt which had Langfield scrambling across his goal.
But just five minutes later and the Jags' dominance paid off when Lee Mair's effort broke into the path of Conrad Balatoni, who slotted home.
In the 64th minute Higginbotham's right-wing cross was brilliantly executed by Taylor to double the hosts' lead.
But their two-goal advantage was to be halved two minutes later after Rooney got on the end of a Niall McGinn cross to place a glancing header past Gallacher.
However this setback failed to knock Thistle off their tracks and in the 72nd minute they increased their lead when Stuart Bannigan found Taylor, who scored his second goal of the game.
Taylor should have found the back of the net on a further three occasions when in the space of a frantic six-minute period he saw efforts go wide - touched aside by Langfield - and into the side-netting.
For the remainder of the match the play took place in the Thistle half, although they consistently posed a threat on the counter.