Despite a gulf of 141 places between the two in the FIFA world rankings, the game in Chisinau was goalless at half time, but the Dragons managed to open the scoring on 80 minutes through Hal Robson-Kanu.
Aaron Ramsey then made sure of all three points in injury time and, combined with the Republic of Ireland's 1-0 defeat at the hands of Serbia, Wales now sit second in Group D, four points behind the Serbs.
Coleman told Sky Sports News: "It was a win, a good win. Not our best performance over 90 minutes but it was going to be tough. We needed to be patient and not get frustrated. It is hard to come here and break them down. They hit us on the counter a couple of times but the lads did everything we asked.
"That makes it 18 campaign games and one defeat. Sometimes you have to dig a result out, you have to suffer and come through it. You have to show heart and courage and we have shown that. we are still in the mix.
"You have to fancy Serbia but we have to try and get second. Still very exciting for us and everything to play for. Bring it on and make sure we take the red wall with us. We have to be better in our all-round play though. We will need our perseverance and resilience again."
Wales travel to Georgia on October 6 before finishing off their campaign against the Republic of Ireland in Cardiff three days later.