Roma turned pre-match predictions on their head by handing Sassuolo their second-biggest home defeat of the season
Juventus were given an extra incentive to move further clear of their scudetto rivals when AC Milan, who stunned the champions 1-0 last weekend to close the gap to two points, crashed 3-0 at Genoa on Tuesday.
Roma turned pre-match predictions on their head by handing Sassuolo their second-biggest home defeat of the season to walk away with the spoils, although their seventh win of the campaign was tempered by Alessandro Florenzi crumbling to the ground with a suspected serious knee ligament injury.
Although Juventus underlined their credentials with a classy 4-1 win at home to Sampdoria, which saw Mario Mandzukic hit his maiden goal of the season and defender Giorgio Chiellini hit a brace, Roma remain just two points in arrears.
A Napoli win against Juve on Saturday could see Roma go top if they beat Empoli away, but Dzeko played down suggestions they are now Juve's biggest rivals.
He told Sky Sport: "All we're thinking about is winning our next game, but we're happy for this win."
Napoli capitalised on Milan's earlier collapse to move up to third at four points adrift ahead of the sides' clash in Turin this Saturday.
Thanks to a battling 2-0 home win over Empoli, with Dries Mertens crucially breaking the deadlock six minutes after the restart, Maurizio Sarri's men are now just two behind Roma.
"The squad is doing well, if you consider we lost the league's top scorer over the summer, and his substitute in September," Sarri told Premium Sport in reference to Gonzalo Higuain's move to Juventus and the serious knee injury suffered by his replacement, Arek Milik.
Milan dropped to fourth with Lazio moving up one place to fifth after a 4-1 rout of Cagliari that included a superb double from Ciro Immobile and a great, final goal from Felipe Anderson.
Elsewhere, embattled Inter Milan coach Frank De Boer saw his survival hopes boosted by Mauro Icardi's 88th minute winner in a 2-1 home win over Torino that, nevertheless, saw the nervous Nerazzurri miss chance after chance.
De Boer was given the backing of club bosses earlier on Wednesday, but will remain concerned at his side's inability to finish the easiest of scoring chances.
Roma travelled to Sassuolo wary of the Tuscans' formidable home form, and were initially proved right when Paolo Cannavaro fired a bullet header past Wojciech Szczesny on 12 minutes after being left unmarked on the edge of the box.
Roma missed a series of chances to pull the match level, Radja Nainggolan's screamer coming off the crossbar and Dzeko also thumping the bar from a low Emerson cross before the interval.
Dzeko made amends in the 57th minute, latching on to Mohamed Salah's superb cross-field ball to beat Andrea Consigli with a crisp angled drive.
Salah then saw an attempt cleared a metre before the line by Gregoire Defrel moments later, but Roma were soon in the driving seat after Pol Lirola came off the bench to clumsily barge into Dzeko.
The referee pointed to the spot and Dzeko fired into Consigli's top corner. It was his 10th league goal in nine appearances this season and means he remains two goals ahead of Icardi, who has eight goals.
Stephan El Shaarawy threatened a third goal moments later, and although Consigli saved Nainggolan was quick to tap in the rebound.
A spell of torrential rain halted the Fiorentina v Crotone fixture for over half an hour as groundsmen worked to remove excess water from the pitch.
League newcomers Crotone were heading for their maiden Serie A win after a 24th minute opener by Diego Falcinelli, only for Davide Astori to level for the hosts five minutes from time.