Alan Archibald's Irn-Bru First Division champions will host United at Firhill on August 3 as the top flight of the new Scottish Professional Football League kicks-off.
The Tannadice men will be led to Glasgow by former Jags boss Jackie McNamara, while utility man Paton could be joined in the side by playmaker Chris Erskine after both players moved to Tayside on pre-contracts earlier this summer.
Former Thistle skipper Paton said: "I'm not surprised in any way by the fact we've got Thistle first. I said yesterday on Twitter that we'd get them and we did. I should have put money on it.
"It's always the way these things seem to work out. I'm looking forward to the game. I know myself, the gaffer - and to a lesser extent - Chrissy might come in for some stick but we'll take that on board.
"It's just another game as far as I'm concerned and a good place to start. I obviously know the stadium so it will be good to go there in front of a full house with a good atmosphere."
McNamara quit the Maryhill outfit in January to replace Peter Houston as United boss. But he was involved in a bitter compensation dispute with his former employers in the months that followed, with both sides threatening legal action.
The saga was only resolved last week but Paton insists the row would not have added any extra spice to the game as far as the players are concerned.
"As players, we don't really care about what is going on in the background," he said. "We let the chairmen and the boards sort out all the other stuff and we just concentrate on the football side of things.
"The only people at Dundee United who will take special significance from the game at Partick will be me, Chrissy and the gaffer. For the rest of the boys, it will just be another game."
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