Malesani's first assignment since replacing Eusebio Di Francesco in the Sassuolo dugout was a game against his hometown club Verona, who also won automatic promotion from Serie B last season.
Thomas Manfredini made life difficult for the relegation-threatened Neroverde with an own-goal in the 50th minute before veteran striker Luca Toni doubled Verona's lead four minutes from full-time.
Antonio Floro Flores scored a late consolation for Malesani's men but they remain a point from safety ahead of next weekend's daunting trip to Inter Milan.
It would be an insipid first half of football for fans of both clubs as neither side managed to conjure up a meaningful or memorable effort on goal.
Domenico Berardi's early attempt to beat Rafael from distance was the closest Sassuolo came to threatening, with Toni responding with a shot on the volley that sailed well wide.
A frustrating midfield scramble gave way in the 20th minute when Emil Hallfredsson tried his luck from distance, the ball sailing over the bar and, six minutes before the break, Toni repeated the trick after twisting his body in the area.
Visiting fans would be given a reason to be cheerful shortly after the restart as Manfredini contrived to score the own-goal that handed Verona the advantage.
The former Genoa defender was trying to anticipate Toni's movement towards a Hallfredsson cross but instead diverted the ball into his own net.
As unfortunate as Manfredini had been, his mistake provided the game with a much-needed spark and sense of urgency and Verona made sure to take the initiative.
With the hour mark approaching, Juan Iturbe took off at speed towards the Sassuolo area, where only a last-ditch sliding tackle from Paolo Cannavaro stopped the tricky Argentinian picking his spot for goal number two.
Bosko Jankovic whipped his shot just over the bar as Hellas piled on the pressure and, in the 72nd minute, Gianluca Pegolo made a desperate double save as his team-mate Reto Ziegler swung erratically at a loose ball.
Verona continued to push and probe as Sassuolo retreated into their own half in a bid to prevent further damage, and it was the visiting team's tactical approach that paid dividends.
There were four minutes remaining in Reggio Emilia when Juanito Gomez lobbed the ball into the area for Toni to clip home underneath the onrushing Pegolo.
Celebrations among the visiting fans were then muted, briefly, as substitute Floro Flores headed home a free-kick two minutes into stoppage time, but it was too little too late for Sassuolo.