Victory lifted Wolves into the top half of the table but this result left Burnley still searching for their first league win of the campaign as they equalled a club record run of four successive Premier League defeats.
The win was no more than hosts Wolves deserved. They dominated and could easily have been at least two goals ahead before Jimenez broke the deadlock in the 61st minute when he turned in Matt Doherty's cross.
By contrast, Burnley rarely threatened and their only notable chances fell late in the match to Johann Berg Gudmundsson.
"I am very, very satisfied," Wolves manager Nuno Espirito Santo told Sky Sports. "We played good football and stayed organised and created chances. Burnley are a good side and stayed in it until the end.
"If there is a 'but', we could be more clinical. But if we can continue to make these many chances, it makes me very proud."
Meanwhile Burnley boss Sean Dyche urged supporters to keep faith with the side, telling the BBC their experience of losing streaks in the Premier League would stand the Clarets in good stead.
"We have been down this road before," he said.
"That is important now so we can realise it (climbing the table) can be done."
The game started sluggishly, with the opening 20 minutes memorable only for an alert stop by Burnley's Joe Hart as the former England goalkeeper reacted well to the threat of Helder Costa's cross.
Wolves dominated from then on, with only some last-ditch efforts from Hart and James Tarkowski denying the home side on the half-hour when Jimenez, Jonny Otto and Doherty all went close to opening the scoring.
Early in the second half, Jimenez missed another good chance when he carelessly shot over with only defender Charlie Taylor to beat.
Jimenez did score with a deft flick from Doherty's cross just after the hour.
That goal was sufficient to give Wolves their first home win of the season and meant Espirito Santo's side had recorded back-to-back successes following a 1-0 victory away to West Ham before the international break.
This defeat, allied to the Hammers' 3-1 win away to Everton later Sunday, left Burnley bottom of the table with just one point from their opening five games.