With a lottery team in the building and a make-or-break road trip looming, the Nets had to have a win Wednesday. And with the game hanging in the balance, Spencer Dinwiddie reached out and seized it.

Dinwiddie took over in the final minutes of a contest that was far too close for comfort, steering Brooklyn to a 113-107 victory over the Cavaliers before 14,177 at Barclays Center.

“There was a moment in the fourth quarter where we were desperate,” coach Kenny Atkinson said. “Even in the third, they had an eight-point lead. I’m glad we kept our cool, though, because the last year or two years ago … the lead would go to 16 or 18. The fact that we kept our cool, weathered the storm and came back was important. We won that game without playing great.”

They won it despite playing downright poorly at times. And they won it largely because of Dinwiddie, who had a game-high 28 points, five assists and four rebounds off the bench.

With Brooklyn having blown a 16-point cushion and clinging to a 96-94 lead with 7:20 left, an advantage that was tenuous at best, Dinwiddie sparked the decisive 14-0 run.

Dinwiddie had nine points and two assists on 3-of-3 shooting in the spurt. Rodions Kurucs chipped in with two points, three rebounds and a block in the run, and the Nets harassed the Cavs into 0-for-6 shooting with a turnover. Dinwiddie’s finger roll made it 110-94 with 3:26 left and the Nets easily killed the game off.

“We tightened up the screws. Fortunately we got enough stops and converted on the other end,” said Dinwiddie, who pushed the pace and attacked with abandon.

“Being a young group and finally being healthy we’re going to continue to find ourselves. It’s been an exploratory process this whole season, and we’re hopefully entering the final phase of that. We can tighten the screws and get to where we need to go over the last 17 games and be a force in the playoffs.”

The Nets (34-33) are a percentage point out of sixth in the East behind the Pistons, whom they play host to Monday. They will fancy their chances if they can keep getting performances like this from their backcourt trio of Dinwiddie, Caris LeVert and D’Angelo Russell.

Russell had 25 points and five assists, while LeVert had 14 off the bench as a downhill partner for Dinwiddie. Jarrett Allen added 15 points and 11 boards.

“Big time,” Russell said of Dinwiddie and LeVert. “Those guys, I don’t think anybody in the league can stay in front of those two. When they’re getting downhill, making it easy for us on the offensive end, that makes everybody’s job easy.”

Brooklyn led by 11 after one, and 37-22 early in the second before they allowed a 22-7 run to let the Cavs pull even at 44-all.

Leading 64-58, the Nets did see Kevin Love rip off eight straight points to give the Cavs a two-point edge. And Brooklyn even fell behind 84-76 when David Nwaba (22 points) rattled home a corner 3-pointer with 2:11 left in the third.

But they responded with an 11-1 run that spanned the quarters. LeVert hit a 3 of his own, took a charge on Marquese Chriss and finally made a strong drive into contact for an 87-85 lead.

The lead was still just 96-94 lead when Dinwiddie took over with nine points and two assists in that 14-0 run. He found Kurucs for a dunk to make it 100-94 and Joe Harris for a 3 that pushed it to 103-94 with 4:56 left. They closed it out from there.