Despite trailing leaders Arsenal by seven points, United are the only side in the top six to be unbeaten in the past five league games, having recovered from an early-season blip that included a 2-1 home defeat against West Brom.
The managerial transition from Alex Ferguson to Moyes had initial teething problems, but Irwin is full of praise for the strength of character shown by the former Everton boss.
And Irwin – who won seven Premier League titles as well as the UEFA Champions League during his 12 years at Old Trafford – is backing his former club to challenge for top spot and finish strongly in typical United style.
"The first five or six games were tough for him (Moyes)," said Irwin.
"The draw wasn't the kindest, playing Chelsea, Liverpool and Manchester City. Three top teams in the first five games wasn't easy. But it has taken time.
"Our league form has picked up in the last six or seven games. We're a team in top form at the moment.
"We're certainly in the mix, we're a point behind Manchester City, three points, I think, behind Chelsea and Liverpool and seven behind Arsenal, with a lot of tough games to go and still over two thirds of the season to go.
"So we're very much in the mix. It's been good, the last two or three months.
"If you hang in there, traditionally United get better in the second half of the season.
"I don't think you're going to need 90-plus points, which has been needed over the past few seasons to win the league.
"I think it's going to be lower than that this year with teams beating each other and the likes of Southampton coming on the scene, who have done very well.
"Everton have always been a threat and will take points off teams. So it's going to be a really interesting Premier League this year."
