Gleeson took three of the wickets, recording figures of three for 16, as Kent were bowled out for just 137 in the Specsavers County Championship Division Two encounter.
Nathan Buck (3-28) and Ben Sanderson (3-37) also bagged three apiece for Northants, who looked to be on top after electing to bowl.
But batting also proved to be a problem for the County, who slipped to 44 for eight before finishing the day on 71 for eight, with Brett Hutton (14no) and Gleeson (12no) in the middle.
"To bowl them out for 137 you think 'great start' but they bowled tremendously in helpful conditions," Gleeson said.
"It's not really brightened up all day, it's stayed overcast and the wicket has been doing a little bit throughout, so, what with the slope to contend with as well, we knew it was going to be difficult when we got to bat.
"When we turned up we felt the wicket looked quite flat and that we were in for a long toil, but it doesn't look that way from the scoreboard.
"The pitch has done a little bit, but nothing out of the ordinary. They were just very tough overhead conditions all day.
"The ball is coming out nicely for all our bowlers at the minute, we're all hitting our straps and creating chances.
"That's all we can really be doing and it was nice for me to be in amongst the wickets again today."
Kiwi pace ace Matt Henry was the main threat with the ball for Kent, claiming six for 31 as his team fought back.
And Henry said: "We were hoping to get a few more on the board than we did with the bat, so we came out needing to be patient with the ball and create pressure, because not conceding runs was crucial as well.
"It was good to take eight, but getting their next two wickets early tomorrow will be crucial as well.
"I was trying to keep the stumps in play as much as I could and challenge the defence of their batters.
"I did enough to create doubt in their minds, but it was a funny day because I don' think what happened today is a true reflection of this pitch.
"The odd ball does so a bit, and that created doubt, but more often it was the straight balls that were doing the damage."