Chasing a challenging 163 for five set by Zimbabwe, Stirling (60) and skipper William Porterfield (31) got Ireland off to a blazing start and shared 80 runs off just 8.2 overs for the opening stand to set the platform for the win.
Stirling's 60 came off just 34 balls with the help of nine boundaries and one six, while Porterfield laced his 23-ball knock with three fours and one hit over the fence.
Going strong at 100 for two, Ireland lost their next five wickets in a hurry to make life difficult for themselves towards the end with medium-pacer made Tinashe Panyangara (4/37) doing the bulk of the damage.
After Stirling's dismissal, Ed Joyce (22), Andrew Poynter (23) and big-hitting Kevin O'Brien (17) did the bulk of the scoring but failed to ensure the victory for Ireland as they all became victims of Panyangara.
But Ireland finally managed to scamper home in the final delivery of their innings with Stuart Thompson remaining unbeaten on three off six balls.
Earlier sent into bat, Zimbabwe rode on skipper Brendan Taylor's 46-ball 59 to reach 163 for five from their alloted 20 overs.
Apart from Taylor, Elton Chigumbura (22 not out), Hamilton Masakadza (21), Sean Williams (16) and Vusi Sibanda (16) made significant contributions with the bat.
Left-arm orthodox bowler George Dockrell (2/18) and off-spinner Andy McBrine (2/26) shared four wickets between them for Ireland. Ireland will play UAE in their next qualifying match on Wednesday here, while Zimbabwe will be up against Netherlands.