The 22-year-old striker, who has had loan spells at Hamilton and Morton, made his first SPL start in his fourth appearance this season and was voted sponsor's man-of-the-match in a comfortable victory.
Mowbray said: "In my mind he has cemented his place in the first-team squad so let's hope he can push on.
"His overall performance pleased me. He is a young guy who deserves an opportunity.
"Every day in training, you see he has a great enthusiasm for the game and he is good off both feet so I'm delighted for him."
With his contract ending in the summer, McGowan knows he has picked the perfect time to come to the fore.
He said: "That's a big boost to hear what the manager said. I only found out on Friday that I was starting. I was obviously a bit nervous but I have been playing well with the reserves and training a lot with the first team.
"I've waited a long time for it. I was starting to become disillusioned. In the last month or two I have been there or thereabouts.
"But last week the manager told me that I would be training with the first team all the time. My contract is up at the end of the season so hopefully things can turn for the better.
"There was some talk a couple of weeks ago (about a new contract) but nothing yet. I will have to keep going."