His struggling side came into this match without a win in nine games, their worst sequence at this level for 21 years, but they blew away City in a fantastic first half thanks to goals from Sylvan Ebanks-Blake, Bjorn Sigurdarson and a Kevin Doyle double.
Doyle came very close to his hat-trick after the break and Roger Johnson hit the crossbar before Neil Danns' classy goal in the 85th minute gave the City fans something to cheer about.
Derek McInnes made just one change as he looked to lead City to a victory over Wolves for the first time in 19 years with Ryan Taylor replacing Stephen Davies up front.
Solbakken shuffled his pack following the midweek home defeat to Millwall with captain Karl Henry returning to the side after suspension along with Kevin Foley and Ebanks-Blake.
It was Wolves, 19th in the table coming into this match, who started the brighter and they should really have taken the lead in the fourth minute when Ebanks-Blake missed a gilt-edged chance after Bakary Sako's low cross found the striker unmarked in the box but he somehow put his effort wide.
The Robins are the only team in the Football League yet to keep a clean sheet and so it was no surprise when Ebanks-Blake opened the scoring in the 20th minute with his first goal in nine games. Fontaine cleared a corner only as far as Stephen Ward, whose fine volley was diverted in by the former Manchester United trainee.
The lead was doubled just four minutes later when a fine move ended with Doyle bundling Sigurdarson's cross from the right flank past Tom Heaton for his first away goal since February.
The Ireland international had only scored three times in 19 appearances this season but netted his second in just 16 first-half minutes with a wonderful solo goal. The former Reading striker picked the ball up in his own half and ran unchallenged before slotting home.
And just a minute before half-time, the visitors made sure of their first three points in 10 games with another fine move, finished off with a left-foot shot across Heaton from Sigurdarson after Ebanks-Blake teed him up.
McInnes introduced Sam Baldock at half-time but Wolves picked up where they left off with Doyle coming close to a hat-trick on two occasions, the first was cleared off the line by Matthew Bates and his second effort was saved by Heaton.
City were then inches away from finding themselves five down when Johnson met a corner with a header that bounced off Heaton's bar. Baldock then had his side's best chance of the game when Foster found him 10 yards out but he could not test Carl Ikeme.
Danns had a low drive saved by the Wolves keeper before the Leicester loanee netted a consolation in style from 25 yards with five minutes to go.