He blew staff away with his GPS numbers soon after arriving, despite not playing a match since August due to Auckland's lockdown and quickly became part of coach Jim Goodwin's plans once his transfer was officially processed in January.
After substitute appearances against Dundee United and Aberdeen, Greive got his first start against Hibernian last weekend, before his eye-catching performance in the 2-1 win over St Johnstone on Wednesday morning (NZT).
Greive popped up at the far post to score the decisive goal in the 49th minute and drew rare praise from manager Goodwin after the match.
"I thought he was different class, honestly I really did," Goodwin told the club website. "Through injuries and what have you, Alex Greive has found himself in the team and he has been superb to be honest."
"Considering the lack of game time he has had up to now, apart from the few sub appearances he has had for us, starting the game at [Hibernian] and staring the game tonight, playing his first full 90 minutes for the club. I thought he was man of the match."
Greive was understandably delighted.
"I'm buzzing, mate,'' he told the club website. "I can't put it into words. The most important thing is getting a win. The boys dug deep, we're moving now.''
With less than three months in a professional environment, it's hard to think of another New Zealander that has made such an immediate impact, especially given his background.
"100% per cent I reckon I'm a late bloomer," Greive told the Herald last month. "Everyone who knows me knows how small and stuff I was all through. It wasn't until I went to America (to play at College) when I was 18, I started to develop physically a little bit."
"So I always believed in myself and [the dream of] playing professional football. It was just about plugging away and biding my own time and wait for the right opportunity"
Greive has taken his chance superbly and his arrival has coincided with an upturn in fortune for the Buddies, who have won four of their last five games to rise to sixth.
Their next match is a Scottish Cup fifth round clash with Kelty Hearts on Sunday, before facing Livingston in the league the following week.