The Timberwolves appeared to be on their way to a much-needed, come-from-behind victory Tuesday night at Target Center to resusitate their NBA Cup hopes.

Down by 17 at one point in the third quarter, the Wolves went on a 16-0 run to get back into the game, and led by five with two minutes to play in the fourth.

And it all went wrong from there.

Poor offensive possessions down the stretch allowed Houston — which made just six of its 22 shot attempts in the fourth quarter — to tie the contest. Anthony Edwards’ potential game-winning shot attempt in the closing seconds rimmed out.

It was all Rockets in the extra session.

Minnesota’s late-game offense — which has been a salve for many wounds thus far this season — failed the Wolves in overtime as Houston pulled away for a 117-111 victory at Target Center.

Minnesota has lost three straight games and is 1-2 in NBA Cup play, meaning its hopes of advancing to the knockout round are effectively kaput.

Houston controlled the first three quarters of Tuesday’s affair with a dominant defense that resembled what Minnesota touted a season prior. Meanwhile, the Wolves surrendered layups and open 3-point attempts at will.

Rookie guard Rob Dillingham provided a spark for Minnesota when it needed it most. He finished with 12 points, seven assists and five rebounds. But the rookie also committed a costly turnover late that led to Houston’s tying layup near the end of regulation.

Anthony Edwards led Minnesota with 29 points and 10 rebounds.