Steven Thompson's brace and Dougie Imrie's first Saints goal proved enough to conquer the Dark Blues, who had only a Ryan Conroy penalty to show for their trip.
Lennon said: "I'm delighted, not just with the victory, but also the performance. I know you get the same three points but the manner in which the boys went about their business was great.
"The commitment from the boys from the first minute was terrific and they got their rewards today, which they deserved.
"There was a real hunger in the players' eyes and you could see before the game that they were itching to get out there. I thought we handled everything Dundee threw at us. Hopefully we can now kick on from this."
He added: "This group of players are certainly better than what their current league position shows. But you can't hide from what the table is reflecting.
"Words become cheap unless you turn them into actions and we did that today. I'm delighted for them."