Samp always had the psychological edge after opening the scoring through Gianluca Sansone inside 18 seconds but Sassuolo are fighting for top-flight survival and levelled through Alessandro Longhi.
The chances were shared in a frenetic second half and it was Stefano Chuka Okaka who grabbed the goal that Samp needed to reach ninth place in the Serie A table.
Defender Vasco Regini saw red at the death, but it did not affect the final outcome.
Nine is the number of matches Sassuolo have lost in their last 11 attempts and they now lie five points from safety with only eight games remaining.
Sassuolo goalkeeper Gianluca Pegolo was still checking his posts and throwing his water bottle into the net when Sansone scored the first goal of the game.
The clock read 18 seconds as the former Neroverde man waltzed into the area to blast home an uncontested daisy-cutter.
Sassuolo had no choice but to respond well and almost levelled through Simone Zaza, who lacked accuracy when trying to steer home Francesco Magnanelli's free-kick.
Angelo Da Costa then blocked Zaza's cross-cum-shot but, in the 16th minute, Sassuolo found an equaliser.
It would be a first Serie A goal for Longhi as he picked up Zaza's cross to beat his marker and slip the ball into the net.
Samp's players were convinced the left-back had been in an offside position, but the goal stood.
After the early burst of action the life fizzled out of the first half and the most notable incident before the break saw Sassuolo defender Paolo Cannavaro replaced by Pedro Mendes due to injury.
The hosts appeared more likely to score when play resumed and Lorenzo Ariaudo went particularly close when trying to nod home Domenico Berardi's cross.
Da Costa found himself making a desperate save when Magnanelli rifled the ball down his throat and, in the 66th minute, Samp forged ahead once again.
Pegolo was perhaps to blame as he misjudged his run from the goal-line to cover Okaka, who converted Eder's assist with relative ease.
Sassuolo substitute Antonio Sanabria might have restored parity with a sighter that forced a low save from Da Costa, but the chase steadily began to slip away from the home team.
The Genoese club should have put their hosts to bed two minutes from time but Eder somehow managed to miss the mark when fed in the six-yard box by sub Manolo Gabbiadini.
Samp were also able to survive the late dismissal of Regini, who came a cropper when fouling Berardi, to climb to ninth.