The head coach had only collected one point from the three league matches since his return to San Siro in November, however he oversaw a victory in Verona.
Mancini previously led the club from 2004 to 2008.
Goals from Mateo Kovacic and Andrea Ranocchia were enough to give Inter a comfortable victory, althouygh the winning margin could have been wider with better finishing.
Mancini did not mind, though, as recording all three points was much more significant to the 50-year-old.
"It’s an important win, as clearly we are gaining confidence because despite the difficulties of facing Chievo we didn't concede," he is quoted as saying by Gazzetta dello Sport.
"I am fairly satisfied.
"The lads are improving in training and putting that into practice in a match situation."
Mancini turned his attentions to Sunday's clash with Lazio - a club he once played for and coached - and he said he is aware they must keep improving to build on their breakthrough win.
"It's an important game [against Lazio]," he added. "Winning would mean finishing the year on two straight wins and that would be good for morale.
"But we still have work to do."
Monday's win sees Inter climb into 11th place in Serie A, but they remain six points behind third-placed Lazio.
