But it was not all plain sailing for Moyes' side as, just as they had against Romanian side FCSB a week ago, they conceded the first goal, this time through a neat finish by Kasper Kusk.
And they were hanging on for the final 15 minutes after Soren Tengstedt pulled one back, before eventually making it two wins from two in Europe this season to top Group B.
Moyes told BT Sport: “Bits and pieces I liked, bits and pieces I didn't. When it was 3-1 it should have been comfortable.
“We started making poor decisions on the counter attack, which I'm annoyed about, and a couple of poor decisions defensively. But look, we got the job done. Away from home, winning in Europe is not easy.”
Dawson was making his first start of the season after recovering from an injury sustained over the summer.
He said: “They made it difficult for us towards the end. The performance wasn't great. It's a difficult pitch to play on, it was a bit sloppy but we got the three points.
“They're a good side and play great football. They know the pitch better than us. At times we were sloppy but we got the job done.
“It's great to be back. It's been a while.”
The defender was close to leaving West Ham on deadline day but a move to a midlands club, where he could be closer to his family, failed to materialise.
Additional reporting by PA.