The home side won the Clydesdale Bank Premier League encounter 1-0 with John Sutton coming off the bench to score the winning goal four minutes from the end.
A young Hearts side had dominated the game but failed to find a way through a resolute Dundee defence until a late double substitution finally broke their resistance.
"The players were a bit tired and bringing on those fresh legs got us the goal," said McGlynn. "We're delighted that we got the victory.
"I think we deserved three or four more goals. I felt we were in control of the game, but obviously we hadn't taken the chances until that point.
"In fairness to us I thought (Dundee goalkeeper) Rab Douglas had an excellent game, he always seems to have a good game against us.
"We had many young players out there on the pitch, just as we did on Saturday.
"I said when I came in that there would be no better time to be a young player at Hearts. There are more and more appearing in the team and that makes our bench more experienced because of that.
"You saw we were able to turn to Sutton and Novikovas, but we also had Andy Driver, Medhi Taouil and Darren Barr. These lads will respond and it should make the whole squad stronger."
- Sports & Recreation