Ireland elected to bat on Monday (Tuesday AEDT) and for the third game in a row it proved far easier scoring during the day than under lights as they posted 9-284 in their 50 overs.
South Africa battled from the start of their reply and were bowled out for 215.
Stirling and Andy Balbirnie (45) put on 101 for the first wicket, with Harry Tector scoring a fine 60 from 48 balls at the tail end of the innings to boost Ireland's score.
South Africa toiled in the heat, but series leading wicket-taker Lizaad Williams took 4-56 in another impressive display of seam bowling.
They rested most of their regular players for the series and were further depleted by injury to the point where batting coach JP Duminy was forced to field in sweltering heat some five years after he played the last of his 81 T20 internationals.
Ireland had their opponents reeling at 3-10 in their reply, a position from which South Africa never recovered.
Jason Smith, playing in his second ODI, led a lone resistance with an eye-catching 91 from 93 balls.
South Africa won the first two matches in the series by 139 and 174 runs respectively, as winning the toss and batting first proved the key to success at the Zayed Cricket Stadium.
