Brett Favre dinked and dunked passes down field, and the New York Jets’ offense hardly resembled the powerhouse it was in its last game.

Sure, it wasn’t pretty, but that didn’t matter much to the veteran quarterback. He still left the field with a 26-14 victory over the winless Cincinnati Bengals on Sunday.

‘‘I don’t believe in ugly wins,’’ Favre said. ‘‘I believe a win’s a win. That one felt as good as any win I’ve been a part of in recent memory.’’

Thomas Jones ran for two touchdowns, including a 1-yarder late in the game, and caught a pass from Favre for a score.

The defense also stymied the Bengals’ rushing attack and fill-in quarterback Ryan Fitzpatrick.

‘‘It wasn’t our best performance on offense,’’ Favre said, ‘‘but it was a win.’’

The Jets (3-2) improved to 3-0 in games following a bye under coach Eric Mangini, but this one was far from easy. With New York holding a 20-14 lead, the Jets needed a 10-play, 41-yard drive engineered by Favre that ate up the clock to seal the victory.

‘‘It was move-the-chains types of throws,’’ he said.

Favre, coming off a six-touchdown performance in a 56-35 victory over Arizona, was 25-of-33 for 189 yards and a touchdown, but also had two interceptions and lost a fumble that was returned for a score.

‘‘I’m not here for stats,’’ said Favre, who turned 39 on Friday. ‘‘I’m here for wins.’’

Jones finished with 17 carries for 65 yards and had his first career three-TD game for the Jets, wearing their navy and gold throwback New York Titans uniforms for the second straight game.

‘‘Last (game), we threw the ball really well and scored a lot of points and today wasn’t that exact same situation,’’ Jones said. ‘‘We had to kind of grind it out a little more. The good thing is we’re able to do both.’’

Fitzpatrick couldn’t get much going for the Bengals (0-6) in place of ailing Carson Palmer. He was 20-of-33 for 152 yards as Cincinnati dropped to 0-6 for the third time since 2000.

‘‘O-and-anything stings,’’ linebacker Dhani Jones said. ‘‘We just want to get the bad taste out of our mouths. Oh-and-6 is not a position anybody wants to be in.’’

The Bengals gained just 43 yards rushing, with Fitzpatrick’s 23 leading the way.

‘‘Everyone will say that with a backup in there, we need to run the ball better. We will,’’ said Fitzpatrick, making his second start in three games with Palmer resting a sore right elbow. ‘‘It was a struggle out there today. We have to go back to the drawing board and figure it out.’’

Despite their struggles, the Bengals were still in it late. The Jets had a third-and-4 from the Bengals 7 when Favre hit Chris Baker for 6 yards. Jones followed with a 1-yard rumble into the end zone with 2:22 left and the 2-point try fell incomplete, making it a 12-point game.

That proved to be too much for the Bengals, who were unable to make big plays against the Jets defense.

‘‘We’ve got to do better,’’ Bengals coach Marvin Lewis said. ‘‘It’s not good enough.’’

Cincinnati took a 7-0 lead on the third play from scrimmage, when Antwan Odom sacked Favre and forced a fumble. Chinedum Ndukwe picked it up and ran 15 yards into the end zone to give the Bengals the lead 1:24 into the game.

It didn’t last long. New York tied it with a 2-yard touchdown reception by Jones.

‘‘It always feels good to get touchdowns, get into the end zone and contribute to the team winning,’’ said Jones, who had two TDs all of last season.

The score capped a strange drive during which Favre had thrown two other touchdown passes that were called back by penalties.

‘‘We’re not going to throw six touchdown passes every week,’’ Favre said. ‘‘We might throw three on one drive, which was different, but we’ve got to be able to win games like that.’’

After Jay Feely gave the Jets a 10-7 lead with a 38-yard field goal early in the second quarter, Fitzpatrick fumbled when he was sacked by Hank Poteat. Calvin Pace recovered the ball and, two plays later, Jones ran it into the end zone from 7 yards.

Fitzpatrick’s 1-yard run made it 17-14 with 8 seconds left before halftime.

‘‘Everyone wants to go out and blow people out, but realistically that’s not going to happen every week in this league,’’ said Pace, who had one of the Jets’ five sacks. ‘‘Today was a good sign of everybody coming together for a win.’’