The left-arm spinner, who made his India debut against Afghanistan in June, finished with a 10-wicket match haul, including six in the second innings.
"He has been bowling magnificently, even in the first match he played in India and in this match as well," Gill said of the Rajasthan bowler.
"He looks like a promising guy and someone who can play for India for a very long time."
Suthar narrowly missed out on a hat-trick after dismissing Sonal Dinusha and Prabath Jayasuriya with successive deliveries, although he claimed a third wicket, Lahiru Kumara, in an eventful over.
Devdutt Padikkal was adjudged player of the match for his majestic 167 in the first innings, further suggesting he could be the answer to India's search for a reliable number three batter.
"He was magnificent to watch," Gill said of Padikkal, who made a fluent 44 in the second innings.
"It's important to get hundreds, but even after getting a hundred, how he carried on and got a big one for us, that's the difference between being in a competitive match and being in a comfortable position.
"His knock in the second innings as well, the way he played and the way he dominated the spinners was a treat to watch."
Drafted in as a replacement for the injured Sai Sudharsan, Padikkal seized his opportunity, smashing his maiden Test hundred in just his third match.
"I couldn't have asked for anything better," Padikkal said.
"The game was amazing. I think we played some really good cricket and really happy with the win."