Stirling hit 60 off 34 balls with nine fours and a six, and despite a late flurry of wickets Ireland cruised to 164-7 off the last ball after Zimbabwe scored 163-5.
Stirling and captain William Porterfield (31) laid a solid platform in the run chase by adding 80 off 50 balls before fast bowler Tinashe Panyangara grabbed 4-37 but could not stop Ireland from scoring four runs in the last over.
"Just glad we got over the line," Stirling said. "We have played all over Bangladesh in the recent past (but) I wasn't really looking toward the final stages of the match."
Earlier, Zimbabwe captain Brendan Taylor top scored with 59 off 46 balls as spinners George Dockrell (2-18) and Andy McBrine (2-26) struck regularly to restrict their opponents.
Ireland have two relatively easy opponents in the remaining two group matches -- United Arab Emirates and the Netherlands -- with the top team set to join South Africa, Sri Lanka, New Zealand and England in Group 2 of the main round.
Ireland 164-7 (Paul Stirling 60, William Porterfield 31; Tinashe Panyangara 4-37) def. Zimbabwe 163-5 (Brendan Taylor 59, Elton Chigumbura 22 not out; George Dockrell 2-18, Andy McBrine 2-26) by 3 wickets.