Kevin O'Brien's 25-ball 50 and Gary Wilson's 80 helped Ireland pull off a narrow victory.
O'Brien came out to bat at No. 7 position and slammed right boundaries and two sixes to complete his half-century.
Balbirnie was out playing a stiff shot to the subtitle fielder Saqlain Haider.
Joyce was later dismissed on 37 by Javed.
Porterfield was bowled and O'Brien was out LBW to Tauqir.
Ed Joyce was not able to make the most of a bizarre let-off early on.
The ball, bowled by Amjad Javed, swung in late and beat Joyce's forward prod before hitting the off stump.
Stirling was out edging behind to Swapnil Patil to leave Ireland at four for one.
Anwar came to the wicket when UAE were struggling at 78 for four in the 21st over.
Anwar also became the first UAE batsmen to score a century in World Cup history.