Goals from Gary Harkins, Steven Thompson and Sean Kelly secured the win over the Championship side in the fourth round replay as memories of the home side's stuttering start to the season continue to fade.
"We're delighted to be through to the next round. Queen of the South were very energetic and I'm surprised where they are in the Championship table at the moment," said Lennon.
"That's a fifth clean sheet in nine games now and that shows how hard we're working as a team.
"What they threw at us we coped with very well. Marian Kello only had one save to make.
"Gary Harkins shows the true quality he has, He's never been out of my plans, it's just the boys that have come in have held the jersey. I was also delighted for Sean Kelly to get his first senior goal."
Queen of South manager Jim McIntyre added: "We looked nervous and St Mirren were deserved winners tonight.
"That's a sore one because we're better than that. St Mirren made the most of their second opportunity, we didn't."