James Vrionis tackled London Gaskin for a safety in the third quarter, the two points turning out to be the difference as Jesuit held on.
Devyn Freeland led the Tigers defense with two of a season-high four interceptions. They returned one 55 yards for a touchdown.
The Tigers raced out to a 7-0 lead on a pass from Vincent Testaverde to Christian Williams. A 12-yard touchdown run by Malik Davis put the Tigers up 14-0 before Trinity answered with a 2-yard touchdown run by Gaskin.
A field goal by Rhett Waldron put Jesuit up by 10. But the lead was short-lived as the speedy Gaskin took a swing pass 78 yards to cut the lead back to three. Jesuit added to its lead on a 1-yard touchdown run followed by Gaskin's interception return to put the it up 31-14 at the half.
Following the safety early in the third, the Celtics (4-3) scored twice to narrow the gap to 33-27. Waldron hit a 36-yard field goal to put the Tigers up by nine, but Trinity again answered on a 31-yard keeper by quarterback Reid Carlton.
The teams traded possessions in the fourth quarter with Jesuit clinging to a two-point lead.
"It was tense. I'm not going to lie," Jesuit coach Matt Thompson said.
"But we tried to stay poised and just run our offense."
Trinity got the ball back with less than a minute left, but Travell Harris' interception sealed the victory for the Tigers (4-3).