Wilson, who sat out last week, looked extremely rusty early on, almost throwing an interception from his first pass and then giving up a pick that presented Trevor Lawrence with a short field for the first touchdown of Sunday's game.
Having capitalised on that mishap, however, the Jaguars failed to make the most of a sloppy Broncos display thereafter.
Although Denver had an alarming 10 penalties for 71 yards at halftime, they trailed only 10-7, with a Lawrence pass picked on the goal line by Justin Simmons before Wilson led the Broncos up the field late in the second quarter for Jerry Jeudy to score.
Pressure had again been building on Wilson and coach Nathaniel Hackett up to that point, but a 98-yard drive early in the second half allowed Melvin Gordon to run in and secure the Broncos a first lead.
Lawrence, rather than Wilson, had struggled badly since his earlier interception, but Travis Etienne Jr. gave the Jaguars hope of a first win since Week 3, adding a touchdown to his 156 rushing yards.
Instead, Wilson came to the fore again with a 47-yard pass to K.J. Hamler that set up the game-winning drive, finished off by Latavius Murray before Lawrence threw a second pick to K'Waun Williams, ensuring there was no route back into the game for Jacksonville.