Norway forward Solbakken has barely featured since moving to Roma in January, but his well-taken low strike on the stroke of halftime was just enough to win a tight contest.
Mourinho said before the match that he was forced to play Solbakken as Paulo Dybala and Lorenzo Pellegrini had to sit out the match with the hope they will be available for Thursday's Europa League decider with Salzburg.
And the 24-year-old made sure that Roma would finish the weekend in the Champions League places, above champions AC Milan on goal difference.
Roma also lead Lazio by two points, knocking their local rivals out of the Champions League places after they had briefly moved into the top four following a 2-0 win at Salernitana earned with a Ciro Immobile double.
A second defeat since the turn of the year leaves Verona inside the bottom three, two points behind Spezia who were beaten 2-0 by Juventus.
However they will be encouraged in their fight for survival by another strong performance which probably deserved more reward.
Immobile on target
Immobile moved another place up Serie A's all-time scoring charts with his double in Salerno which took him to 191 goals in Italy's top flight.
The Italy forward is now No 8 above Swede Kurt Hamrin, who scored most of his 190 goals while playing for Fiorentina between 1958 and 1967, after tapping in Lazio's opener from Adam Marusic's cross on the hour mark and then slotting home a perfect penalty.
Immobile has struggled with injuries but is on eight league strikes for the season, the 32-year-old needing another 14 strikes to draw level with icon Roberto Baggio.
"Our feeling in training over the last few days was that Immobile was improving physically," said Lazio coach Maurizio Sarri.
"Thursday gave him a mental boost so now we need to get the best out of him."
Salernitana, playing their first match under new coach Paulo Sousa after sacking Davide Nicola, have won just one game since the end of October and are four points above Verona.
Lazio are one point above Atalanta, who drop down to sixth after falling to a shock 2-1 home defeat to promoted Lecce.
Harsh defeat
Marco Baroni's Lecce are 13th and 10 points above Verona while Atalanta are three points behind third-placed AC Milan, where Gasperini's team play next weekend.
One place behind Atalanta are Juventus, who are now nine points away from the European spots after their third league win on the bounce.
Juve would be second, level on 47 points with Inter Milan had they not been slapped with a 15-point penalty last month for what the Italian Football Federation ruled was illicit transfer activity designed to artificially boost their balance sheet.
Instead they are seventh and awaiting a decision on their appeal against that punishment, Moise Kean and substitute Angel Di Maria scoring the goals in each half which claimed the points at the Stadio Alberto Picco.
Defeat was harsh on Spezia, who are waiting for Leonardo Semplici to become their new coach after sacking Luca Gotti, as they had Juve on the back foot for large chunks of the match and were twice denied by super Mattia Perin saves in the second half.