Doolan got the only goal of the game as the Jags beat Morton 1-0 at Cappielow and Archibald's side avoided a potential banana skin.
There was little between the teams in a competitive affair, with Doolan's clinical finish just before half-time proving the winner for the top-flight outfit. The striker has been overlooked in favour of summer signing Ryan Stevenson so far this term but came to the fore when it mattered most as he netted on his first start of the campaign.
Archibald said: "He had not started so far this season so he had a point to prove. I've spoken to him before and did so again during the week.
"He showed what he can do tonight. He got a very good goal and a goal at a crucial time. He needed a run-out to get some match sharpness.
"Dools will get his chance. We know how good he is and he scores goals."
While Thistle escaped unscathed from a tricky tie against the Ton, Greenock gaffer Jim Duffy was left to ponder what might have been.
Striker Stefan McCluskey passed up two golden chances either side of the break and was furious when referee Stephen Finnie denied him a penalty when he appeared to tangle with keeper Paul Gallacher.
It was a major let-off for Thistle and Duffy insists the whistler made the wrong call.
He said: "I will be kind and say it was a very contentious decision by the referee to book Stefan. If you looked at their bench, their goalkeeper and their players, they thought it was a penalty as well.
"The first thing Alan did was scream at his defenders for not dealing with it.
"I think it was a penalty. I think it was a poor decision."