The Italian's side-footed finish following good work from Nelson Semedo and Luke Cundle rounded off an encouraging display despite a slow start.
Willy Boly's early exit with a left-leg injury will be assessed with Lage's men set to face Las Palmas on Monday before flying back to the UK.
Bruno Lage made just two changes from last weekend's defeat at Crewe with Joao Moutinho and Romain Saiss replacing Fabio Silva and Max Kilman in the starting line-up.
New signings Jose Sa and Yerson Mosquera along with the returning Ruben Neves and Semedo were among the 15 named substitutes.
Betis started the brighter of the two teams with Wolves sloppily giving the ball away on a number of occasions - Taylor Perry and Rayan Ait-Nouri being the chief culprits.
Only excellent covering tackles by Saiss (twice) and Perry himself keeping the visitors on level terms.
Wolves were dealt an early blow with Willy Boly forced off early with what appeared to be a left hamstring issue - Kilman coming on to replace the Ivory Coast international.
And it was the substitute who almost had an immediate impact, heading over from close range.
Morgan Gibbs-White then put through Raul Jimenez through on goal only for the linesman to raise his flag, but replays suggested it was a poor call as Wolves finished the half the better side.
Lage made three changes at the interval with Sa, Neves and Semedo on for John Ruddy, Perry and Moutinho.
Wolves looked to press higher up the pitch and were more threatening from the off.
Ait Nouri impressing along with Jimenez and it was the latter who found Neves with a lovely ball.
The Portuguese international rifled a 25-yard effort that was well saved by Rui Silva diving low to his right.
More changes for Wolves who changed from a back four to a five following the introduction of Mosquera making his debut, Luke Cundle, Fabio Silva, Christian Marquez and Patrick Cutrone.
Silva almost scored a stunner lobbing the keeper from 30-yards connecting with a well-flighted ball over the top, but Cundle may have been better positioned inside the box.
Wolves took the deserved lead late on, Cundle with a wonderful ball to an advancing Semedo who ran with authority and aggression down the right before delivering a pin-point cross for Cutrone to side-foot home.
The Italian has been constantly linked with an exit, but maybe a new lease of life from Lage could result in the forward staying at Molineux.
Jose Sa calmed any late nerves at Lage enjoyed his first victory as Wolves boss.
Wolves: Ruddy (Sa, 45); Hoever (Semedo 45), Boly (Kilman 17), Saiss (Bueno 76), Marcal (Mosquera 60); Perry (Neves, 45), Moutinho (Cundle 60); Trincao (Marquez 60), Gibbs-White (Silva 60), Ait-Nouri (Otasowie 76); Jimenez (Cutrone 60).