Set a target of 220 runs to win the first of the three-game series, Zimbabwe’s Raza hit an unbeaten 60 off 72 balls with four boundaries.
Ervine also made 60 with his runs coming off 78 balls and featuring five fours.
Earlier, Ireland reached 219-8 in 50 overs after being put into bat with Gary Wilson top scoring with an undefeated 70 from 88 balls and five boundaries.
Ed Joyce also reached a half century, finishing on 53 in an innings which featured one of the game’s only two sixes.
The second game of the series takes place at the same venue on Sunday.