The Paisley side reached the final of the Scottish Communities League Cup with a 3-2 victory over Celtic on Sunday and Steven Thompson's late header earned the Buddies their second win in four days.
Esmael Goncalves latched onto Paul McGowan's through-ball to net on his home debut and open the scoring.
Billy McKay netted his 20th Clydesdale Bank Premier League goal, this one from the penalty spot, a minute before half-time after Conor Newton felled Richie Foran inside the box.
Inverness enjoyed the majority of the possession in the second half, however they were punished for their lack of cutting edge in front of goal with nine minutes remaining when Thompson beat Antonio Reguero after connecting with Gary Teale's pinpoint cross.
"To go out there and continue, more so in the first half, where we left off on Sunday was fantastic and the only disappointment was losing a sloppy penalty on half-time," said Lennon.
"It was a terrific header for the winner from Steven Thompson; we are absolutely delighted that in the matter of three days we have managed to beat the two top teams in the league.
"I thought to a man the guys were fantastic, we played some exceptional football in the first half and the only thing that was missing at times was an end product."
- Sports & Recreation
- Steven Thompson
- Richie Foran