The hosts were at risk of going five league games without a victory for the first time since July 2020, but nervous fans need not have worried as their side started on the front foot.
In fact, they opened the scoring in only the second minute when Daniel Maldini ended a 10-month drought by converting from close range.
Danilo Cataldi then had a strike saved, while Gustav Isaksen and Fisayo Dele-Bashiru both missed the target as the Neroverdi defence struggled to hold back the tide.
They eventually wrestled back some of the momentum, nearly equalising in the 27th minute when Edoardo Motta was forced into a fine save to tip away M'Bala Nzola’s fiercely struck, deflected strike.
That was a precursor of what was to come, with the visitors equalising through Armand Lauriente’s emphatic strike into the top corner that rounded off a slick passing move.
The level scoreline left things evenly poised ahead of the second period, but the chances subsequently dried up.
Ismael Kone had one for Grosso’s outfit, although he blazed over the bar from inside the area, while Dele-Bashiru’s effort at the other end was even more wild, flying into the stand behind the goal.
Arijanet Muric was then tested by Mattia Zaccagni’s curling effort, even if the resulting save was fairly straightforward.
As the clock ticked into the final 10 minutes, the game finally became more stretched.
Isaksen and Matteo Cancellieri could have nicked the points for Lazio, with the latter seeing his low drive from distance tipped to safety. Sassuolo, meanwhile, twice called Motta into action, with the goalkeeper needing to make a fantastic double stop to deny Kristian Thorstvedt and Josh Doig.
Those saves ultimately proved crucial as Lazio nicked it at the death when substitute Marusic was picked out in the middle before nodding home his first goal of the season in injury-time.
The 2-1 scoreline means the hosts registered their first league victory since the end of January, whereas the visitors, who won the reverse fixture 1-0, missed out on registering just a second-ever league double over the Eagles.
Flashscore Man of the Match: Mario Gila (Lazio)