The striker, who swapped Wolves for the Lions in January after five years at Molineux, proved the inevitable matchwinner with a 79th-minute effort after being teed up by on-loan West Brom strike partner Chris Wood.
Wanderers boss Solbakken will be growing increasingly concerned with his side's struggles having now gone nine matches without a win, slipping from third place in the Championship table to 18th.
Wolves were booed off at the full-time whistle, with home supporters having not witnessed a home victory since late September.
The Black Country club went into the encounter second-bottom in a form table which was led by Millwall, who have now won their last four games thanks to Keogh's fifth goal of the season to rise up to fifth place.
The first-half's biggest talking point arrived with 12 minutes on the clock as Danny Shittu brought down Kevin Doyle when moving into the penalty area, but the challenge was deemed to have been made just outside the box by referee Michael Naylor.
Bjorn Sigurdarson came close to connecting with Bakary Sako's cross as the game started to flow from end to end, with Adam Smith then finding the side-netting from the right of the penalty area for Millwall.
But the excitement which dominated the opening half an hour dissipated as the first half wore on, with the game goalless at the interval.
Chris Taylor fired wide from distance within 51 seconds of the restart as Millwall broke swiftly on the counter before Keogh then tried his luck.
Wood came close to getting on the end of a ball into the box as Millwall looked the more likely to make the breakthrough.
Solbakken was given another dilemma as goalkeeper Carl Ikeme suffered a hand injury and was eventually forced off in the 66th minute.
The home side finally enjoyed a second-half shot with 76 minutes on the clock - much to the ironic joy of the home support - as Dave Edwards fired over.
But those supporters were soon watching Millwall fans celebrate as Wood held the ball up well and laid off for Keogh to fire home from 12 yards.
Wanderers substitute Sylvan Ebanks-Blake twice came close to an equaliser but it did not come for Wolves.