Within the opening five minutes Wolves had two big chances but could not find the net, as they dominated possession and the overall tempo of the game.
A much more subdued second half almost ended in disaster when Fulham were awarded a penalty and Aleksandar Mitrovic stepped up to take it – but a strong Sa save saw Molineux erupt.
Wolves pushed for a winning goal in the closing minutes but struggled for attacking inspiration, as they recorded their first point of the 2022/23 Premier League season.
Bruno Lage named an unchanged starting XI following the opening day loss at Leeds and stuck with the 4-2-3-1 formation.
The big news came on the Wolves bench as new signing Goncalo Guedes was joined by two players returning from injury in Nelson Semedo and Adama Traore, as the bench looked a lot healthier compared to last week.
Toti Gomes was also included, as Yerson Mosquera, Hugo Bueno and Joe Hodge missed out.
Fosun chairman Guo Guangchang was in attendance at Molineux, watching his first competitive fixture since before the pandemic. He was also at the friendly with Sporting in Portugal before the season started. Alongside him at Molineux was well-known football agent Jorge Mendes.
Marco Silva also named an unchanged Fulham team who started in a 4-2-3-1 formation.
In midfield was Joao Palhinha, who was offered to Wolves earlier in the transfer window but the club turned it down before he eventually moved to Fulham.
In a boiling Molineux, Wolves got the Fulham defence all hot and bothered as they created a massive chance within just three minutes. A Daniel Podence through ball had Pedro Neto in, but the angle was tight and his shot was saved by Marek Rodak. Neto’s rebound header then bounced across goal and Leander Dendoncker was inches away from meeting it.
Moments later, Wolves once again found acres of space on the left flank as Hwang Hee-chan was played through by Podence. In a similar position to Neto’s chance, the angle was tight, and Hwang’s effort was also saved.
The first chance for striker Mitrovic came after 14 minutes when he met a Neeskens Kebano cross, but the forward blasted his effort over the bar from 15 yards.
The visitors began building some pressure of their own, after Wolves’ dominant start, and were finding some space out wide to put crosses in.
A Nathan Collins clearance resulted in a corner, from which Fulham almost took the lead. Bobby Decordova-Reid had a free header that was destined for the bottom corner but Ruben Neves made a last-ditch clearance to save Wolves.
Just after the half-hour mark Wolves created the biggest chances of the game and should have taken the lead. Neto chased a ball over the top and a collision between goalkeeper Rodak and centre-back Tosin Adarabioyo meant Neto had an open goal. He took a touch, with a tight angle, and then lost it before Podence followed up and fired wide.
Wolves should have entered half-time in the lead but had to settle for 0-0 at the break.
It was a very scrappy start to the second half as both teams mis-placed several passes and struggled for momentum going forward.
Wolves did create another huge chance after 53 minutes, in which they should have scored. A Rayan Ait-Nouri cross fizzed across goal and just evaded Hwang, but Morgan Gibbs-White met it on the slide, from no more than four yards, but blazed over the bar.
Goalkeeper Sa attempted to come for a Fulham corner but missed it, as he was bailed out of trouble by his Wolves defenders who cleared the danger.
After 57 minutes, Wolves made their first move from the bench as Guedes was introduced for his debut, in replace of Hwang.
Wolves’ forwards were interchanging regularly, which saw a combination between a 4-3-3 and a 4-2-3-1, with Gibbs-White dropping into midfield. However, they were struggling to create any clear chances as the performance hit a lull after 65 minutes.
Fulham, when they did get possession, were working it forwards nicely but also struggled to trouble Sa in what was a sustained flat period for the game.
Semedo and Traore made their injury comebacks when they were introduced after 78 minutes as Lage brought on reinforcements in an effort to find the winning goal.
After 80 minutes Fulham were awarded a penalty when a rash Ait-Nouri sliding challenge brought down Decordova-Reid. Striker Mitrovic stepped up to take it but Sa was equal to it and pulled off a strong save.
Molineux was buoyed by that save and Wolves began to pile on the pressure. They played almost exclusively in Fulham’s half in search of a winner.
Neves did play a quick free-kick to put Gibbs-White through on goal, before referee John Brooks pulled the play back for a Fulham injury, to the fury of the Molineux crowd.
A brawl erupted after a cynical foul on Gibbs-White by Mitrovic. The two players came head-to-head before team-mates separated them, and they were both booked.
Wolves kept fighting for a winning goal but were unable to find it, as they had to settle for a point on their first home game of the season.
Wolves: Sa, Jonny (Semedo, 78), Collins, Kilman, Ait-Nouri, Dendoncker, Neves, Gibbs-White, Podence, Neto (Traore, 78), Hwang (Guedes, 57).
Subs not used: Sarkic, Boly, Gomes, Cundle Ronan, Campbell.
Fulham: Rodak, Tete (Francois, 92), Adarabioyo, Ream, Robinson, Palhinha, Reed, Pereira (Cairney, 86), Kebano (Stansfield, 83), Decordova-Reid (Mbabu, 92), Mitrovic.
Subs not used: Leno, Duffy, Diop, Chalobah, Muniz.