Odds are Stephen Colbert will say a prayer before taking over “The Late Show” for the first time Tuesday night.

Behind the scenes, David Letterman’s successor is a devout Catholic who taught Sunday school at his New Jersey church. But Colbert’s methods were a bit different than those of ruler-wielding nuns: He’d strum his guitar in class and stage games of Religious Jeopardy, parishioners of St. Cassian in Upper Montclair told The Post.

It was all in keeping with Colbert’s faith and philosophy. “If Jesus doesn’t have a sense of humor, I’m in huge trouble,” he once told Fordham University students.

Some parishioners failed to recognize the faux-conservative media personality when he volunteered for the teaching gig in 2003.

“On his first day, someone asked, ‘Why is Stephen Colbert here?’ ” recalled Regina Sammon, the church’s education coordinator. “I had no idea he was on cable TV.”

Colbert taught CCD for two years, preparing kids for the sacraments of communion and reconciliation while two of his three children attended religious instruction at St. Cassian.

“He made CCD fun. He taught us through games,” recalled former student Zachary Lepak. “He would lead a ‘Jeopardy’ tournament with facts about the chapter we were studying.”

He could have introduced a new category called Sundae Mass — he even delivered cartons of ice cream to his students.

“On the last day of CCD, Mr. Colbert brought in AmeriCone Dream ice cream for everyone,” Zachary said — referring to the Ben & Jerry’s flavor inspired by Colbert, which he calls the perfect way to celebrate any federal holiday.

Colbert staunchly defends his beliefs. As a young actor in Chicago, he refused to do a scene where a Ritz cracker was referred to as “the body of Christ.”

During a discussion about God and Satan on “The Colbert Report,” a patronizing guest remarked that Colbert must have learned well in Sunday school.

Not missing a beat, Colbert retorted, “I teach Sunday school, motherf–ker.”