Paul Pogba’s 71st-minute goal was the difference as Manchester United edged out Burnley 1-0 at Turf Moor.
The win took Manchester United to the top of the table, three points clear of Liverpool, who they will face on Sunday at Anfield.
Manchester United have not been top of the table in January since Sir Alex Ferguson retired in 2013 and there is now real belief that they could pull off a shock league title win this season.
Osman believes Manchester United physically matched Burnley and eventually their greater quality shone when they needed to up their game and take three points.
He insisted that the celebrations after the game showed that result at Turf Moor could become a huge moment in the season for Manchester United.
Osman said on BBC Radio 5 live: “Manchester United met this challenge by Burnley head-on.
“They were physical in the first half, they challenged for everything and Chris Wood and Ashley Barnes got no real change out of Eric Bailly and Harry Maguire.
“United probably didn’t dominate in the way they would’ve liked, they didn’t pop it around quick enough, but they probably should’ve been ahead with that disallowed goal.
“Second half was more what we expected with Paul Pogba and Bruno Fernandes pulling the strings.
“You felt the way United celebrated that goal and the unity they showed that it was a huge moment for them in their season.”
It remains to be seen what approach Manchester United take when they visit Anfield, where Liverpool have not lost a home league game since 2017.