Solomon’s superb curling effort into the right corner rescued a point for the hosts, who generally underwhelmed as they missed the opportunity to move level on points with fifth-placed Newcastle.
Until the Israel international’s intervention, Wolves had looked on course to claim a valuable three points courtesy of Pablo Sarabia’s sweeping first-half effort.
The Spain winger, who had earlier seen a weak attempt saved by home goalkeeper Bernd Leno, expertly turned in Raul Jimenez’s knock down after twice linking with the Mexico international in the build up.
Had Jimenez been able to turn home a second-half header he narrowly glanced wide the game might have proved beyond Marco Silva’s side, who barely threatened until the closing stages.
The result leaves the Cottagers sixth in the table on 39 points, while Wolves remain 15th, four points above the relegation zone.
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Reaction as Fulham are held by Wolves
A night of missed opportunities
Both sides are likely to come away from this contest with a tinge of regret, with a point hardly an ideal outcome for sides with disparate ambitions this term.
Fulham will look back ruefully on a chance lost to apply further pressure on Newcastle and Tottenham as they look to secure European football for the first time since 2011-12.
However, they did little to merit more, delivering a flat performance that provided little for the home supporters to get excited about until the final 15 minutes when, having levelled, they pressed forward in search of a winner and Carlos Vinicius forced visiting goalkeeper Jose Sa into a superb save.
“Many things were different in the second half, the dynamic of the team and the way we pressed the ball. We didn’t do that well enough from the start,” Fulham boss Silva told BBC Sport.
“It was a reaction that I wanted but that’s how we should have started. He [Manor Solomon] needs to keep doing what he’s doing. He doesn’t have 90 minutes in his legs yet. He has been really important but let’s hope he continues doing it.”
Solomon’s goal-scoring cameo was another step forward for the on-loan Shakhtar Donetsk winger, who only returned in January from a serious knee injury sustained in the first game of the season.
Until he struck Wolves’ only concern appeared to be a second-half injury to forward Matheus Cunha, who was taken off on a stretcher after lengthy treatment following a seemingly innocuous challenge.
With Sa making routine stops from a tame Vinicius header, an Andreas Pereira free-kick and a Joao Palhinha effort, Wolves appeared on course to claim a welcome fifth win in nine top-flight matches under former Spain boss Julen Lopetegui.
Aside from good chances for Sarabia and Jimenez, Ruben Neves also headed wide from Matheus Nunes’ cross with Wolves in control.
But they were eventually made to pay, with the visitors now having dropped 15 points from winning positions this term.
“The match changed after the injury to Cunha. We have the need to get a lot of points to stay out of relegation. It’s going to be a hard and tough task but we have one more today,” Lopetegui told Sky Sports.