Greenwood has this season struggled to hit the heights of a breakthrough 2019-20 campaign, when he scored 17 times, but he has come to the fore in recent weeks after taking his tally to four goals in United's last three Premier League games.
He broke the deadlock on Sunday afternoon with a cool finish and, although James Tarkowski immediately levelled, the 19-year-old academy product's deflected effort proved decisive before Edinson Cavani added gloss to the scoreline.
The aptitude of Greenwood, who began this season being sent home by England days after his senior debut, has startled McTominay but the Scotland midfielder has called on the elder statesmen in the United dressing room, as well as manager Ole Gunnar Solskjaer, to keep the youngster grounded.
"He's a talent that comes along probably every 10 years – but I'd probably say longer, he's that good, the way he finishes, the way he moves," McTominay said of Greenwood on the club's official website.
"It's brilliant to see him play with a smile on his face, that's the way we all know Mason. Now he's starting to score more and more goals which is really good for us.
"For the senior lads, it's keeping his head down and focused every single game and in training, not letting him get distracted by other things that are going on.
"It's important that he really kicks on now and he is doing because he's got a brilliant manager there to really push him."
United left it late to beat Burnley, with Greenwood's second coming in the 84th minute and Cavani netting in added-on time, but a fifth successive league win moved Solskjaer's side to within eight points of league leaders Manchester City.
While McTominay did not dismiss the prospect of overhauling their crosstown rivals, the 24-year-old has urged United to focus on their remaining six games rather than expect City to collapse.
"Funnier things have happened in football," McTominay added. "You've got to keep putting the pressure on, that's our sole focus. It's not about saying 'We're waiting for a wobble' or something like that.
"We just have to keep winning our games, we have to keep pushing ourselves, keep doing what we can do.
"If we're there or thereabouts towards the end of the season – we certainly want to be second – and if we can push them and make them wobble a bit then who knows?"
United's late show handed Burnley a third successive defeat and, after Fulham's draw at Arsenal earlier on Sunday, the Clarets are now just six points above the bottom three.
Burnley manager Sean Dyche was encouraged by what he saw at Old Trafford and has backed them to come through their lean patch.
"I've never lacked confidence or belief in what we do here, that's for sure," he said. "It's about turning performances into wins and tidying up some of the details. Not so much (against United), but in the other games.
"The way we went about it here is another strong sign of us being tough-minded and you need that over a Premier League season.
"It's very difficult to expect to not have some spells in the Premier League where things go against you, we've been very good at coming out of those spells with very good performances. We'll have to do that again."