Rees-Zammit scored the second try for Wayne Pivac’s side after an earlier effort from George North with the rest of Wales’ points coming from the boot of Leigh Halfpenny.
Ireland had lost flanker Peter O’Mahony to an early red card.
“It felt really good to score. It would have been a lot better with 75,000 people here, but it’s always good to score for your country and thankfully we got the win as well,” Rees-Zammit said.
“I wasn’t sure I had scored. I had to look at the big screen to check.
“We needed to try to put a good performance in. It wasn’t the best, but to get the four points was really good.”
We needed to try to put a good performance in. It wasn’t the best, but to get the four points was really good
Rees-Zammit won his fifth cap against Ireland.
He was named in the Wales squad for the 2020 Six Nations but did not make an appearance. He then went on to play four times for Pivac’s men last autumn.
Rees-Zammit’s finish for his try against Ireland was superb after North and Halfpenny had done well to get him the ball. The wing beat the covering Irish defence to the line.
“It’s great to play outside George. We both scored which was a bonus,” Rees-Zammit said.
“It was very nerve-racking. The last five minutes were very tough. Thankfully we got over the line in the end.
“We will bring good momentum into going up to Murrayfield and hopefully we can do a job up there.”