MONROE — Tulane’s long wait for anything resembling success may be over.

In one of the most dramatic one-year reversals imaginable, the Green Wave ran around, over and through Louisiana-Monroe on Saturday night, routing the Warhawks 31-14 at Malone Stadium. Tulane, a two-touchdown underdog, improved to 3-2 for the first time since 2003 and is halfway to becoming bowl eligible for the first time since 2002.

Last season, ULM embarrassed Tulane 63-10 in the Mercedes-Benz Superdome, holding the Green Wave to minus-9 rushing yards and letting quarterback Kolton Browning rest after he put the Warhawks ahead 42-3 with a touchdown drive to start the second half.

This time, Tulane was administering all of the punishment, beating the Warhawks (2-3) with a ground-bound offense and knocking out Browning in the third quarter after going ahead 24-0. The score wasn’t as lopsided as a year ago, but the feeling was about the same.

“It just goes to show how far we’ve come,” Tulane coach Curtis Johnson said. “You could have never told me after we played that game last year we’d be on the road and we’d win this game going away. Our players really believe in what we’re doing, and they didn’t flinch. They had no fear. They came up here, and they took care of their business.”

A year after averaging fewer than 40 rushing yards, Tulane ran right at the Warhawks, gaining 253 yards on 53 attempts. The Wave set the tone with six consecutive rushes on its opening drive, leading to a 56-yard field goal by Cairo Santos, and kept pounding the Warhawks.

Tulane went ahead 10-0 in the second quarter with a 48-yard drive, getting all but 6 of those yards on the ground. Dante’ Butler and Orleans Darkwa had back-to-back 9-yard gains, and Rob Kelley finished the series with a powerful 8-yard run and then a 7-yard effort when he carried defenders into the end zone.

The Green Wave started the second half the same way, moving 75 yards in five plays, with every yard coming on the ground. Darkwa broke loose for a 54-yard gain on a draw play to the ULM 13 — Tulane’s longest since Darkwa’s 64-yarder against Houston on Nov. 10, 2011 — then walked into the end zone for a 1-yard score as the Wave went ahead 17-0.

Darkwa finished with 17 carries for 118 yards in Tulane’s first 100-yard performance since that same Houston game.

“I told (Johnson), ‘If I don’t have 100, put me back in there,’ ” he said. “I really wanted to get it. It feels good, but all the backs played well today. Our goal was 300 yards. We could have done even better, but we just have to carry this momentum on to the next game.”

The Wave defense, which could not stop ULM a year ago, did not allow a point until the game was out of hand in the fourth quarter. Tulane sacked Browning four times, sacked backup Brayle Brown twice and picked off three passes.

Tulane sealed the victory when cornerback Jordan Batiste blitzed and forced a fumble from Browning that flew right into the hands of linebacker Dominique Robertson, who raced 33 yards for a touchdown to put the Wave ahead 24-0.

“Jordan Batiste did a great job of knocking the ball out of the quarterback’s hands,” Robertson said. “He has a bad habit of not tucking the ball away, and it fell right into my hands. I wish I could say I planned it, but I have to give credit where credit is due. That was on Jordan Batiste, and I was in the right spot.”

That was one of five turnovers Tulane forced, matching the number the Wave gave up in last year’s blowout loss to ULM.

“That was what we talked about all summer — we have to turn guys over,” Johnson said. “That was the next step. ... Our players look like football players this year. Last year, I couldn’t say that. All of a sudden they are starting to get some confidence and hit a little bit.”

Browning exited with an unspecified lower-body injury after going 12 for 27 for 134 yards, and ULM coach Todd Berry said it was too soon to know how long he would be out. ULM managed only 26 yards on 24 carries.

“We just studied (Browning) and saw what he liked to do,” said nickelback Derrick Strozier, who had an interception. “It all paid off in the end. The defensive line has been working on getting on the quarterback all week. We knew if we took him out of the game, we had a good shot at winning.”

The Green Wave survived an off night from quarterback Nick Montana, who misfired repeatedly and threw an interception in the first half when he underthrew Kedrick Banks on a deep sideline route. Montana was 7 of 20 for 65 yards, and his lone highlight was a 26-yard touchdown pass to Ryan Grant that put the Wave up 31-7 after Tulane linebacker Kyle Davis recovered a muffed punt.

Tulane did not need much passing with the way the running game was working.

“When Orleans is healthy, he can play with anybody,” Johnson said. “They did some things to stop the pass, and we just kept running it. We are smart coaches, and I was the dummy who kept trying to force throws in. I’ve got to get in the habit of taking what they give us. I didn’t do that tonight, but I thought (Montana) played good enough.”

The Wave also survived some special teams mistakes a week after making plenty of special teams errors against Syracuse. ULM scored its first points on an 88-yard punt return in the third quarter, and Santos, who was perfect on field goals en route to the Lou Groza Award last season, was wide right on a field goal in the second half.

His streak of made field goals ended with a blocked kick against Syracuse, but this was the first one he sent wide of the uprights since the second quarter of the 2011 season finale against Hawaii.

Again, it didn’t matter. After a series of poor first halves this year, Tulane started fast and never let up.

“Coming into the game, we just talked about starting fast,” Strozier said. “A couple of games early on in the season, we came out and gave up points. That was the biggest thing, to start out fast and maintain that dominant effort throughout the game.”