The Bears batted first and thanks to three half-centuries from the top order, set Sussex a daunting 199 for victory before Gleeson was one of several players to impress with the ball.
Opening batter Rob Yates got the Bears off to the perfect start, striking a blistering 54 off 27 balls which included six fours and three sixes before in-form Beau Webster (60) added to his tally for the season with a third 50 in as many games.
Sam Hain then became the third batter in the top four to reach the milestone, scoring an unbeaten 68 off 38 balls to see the Bears to an imposing 198 for three.
Sussex reached 36 without loss in reply and were just behind the required rate at the halfway stage, but the Bears impressed through the middle overs with Gleeson (four for 19) complimented by Usman Tariq (two for 26) and Jordan Thompson (two for 16) as Sussex were bowled out for 122 inside 17 overs.
“We were brilliant throughout,” Gleeson said. “The boys read the wicket really well.
“The way Yatesy [Rob] got us going at the start put them under real pressure. Hainey [Sam] was brilliant and again, Beau Webster was absolutely fantastic. He's in some form at the minute.
“With the ball I was the lucky one to get the wickets, but everybody chipped in and contributed. The way Woakesy [Chris] started, he's didn’t have much luck, but his third over when he came back bowling to the left-handers to the short side was absolutely superb.
“Usman [Tariq] again - brilliant teams are really struggling against him. Mouse [Dan Mousley], very good. Thomo [Jordan Thompson] was just nailing his yorkers and I was just the lucky one to mostly clean up there.”
The Bears have turned their fortunes around in the last three games, producing an outstanding chase against Somerset to get their campaign up and running and winning against local-rivals Worcestershire last Friday prior to tonight’s victory.
Gleeson is confident the Bears can continue their winning run, as they look to make a late charge for the knockout rounds later this month.
“We've shown what we can do,” he added. “We've put ourselves in a position that we've got to win probably every game,” he added. “We might sneak in with losing one, but with the way we've played in the last three games there's no reason why we can't go on a run and win every game.
“It's the start of a busy five days for us so to get off the mark here today in this little period is brilliant and then we go away and we need to recover well.”
The Bears travel to Sophia Gardens on Friday 3 July to take on Glamorgan, with play getting under way at 6:30pm.