Andrea Belotti scored after eight minutes to get the hosts off to the perfect start, as Iago Falque also scored twice to secure the three points for Sinisa Mihajlovic's side.
Francesco Totti scored Roma's only goal - a 55th minute penalty becoming his 250th goal in Serie A - but there was to be no fitting celebration for such a landmark achievement.
The Giallorossi dominated possession for large parts of the contest but Torino showed a great cutting edge on the counter-attack, with Belotti rising early to head home Joel Obi's cross.
Falque then scored from the penalty spot after half-time to double the advantage, before Totti grabbed one back after Diego Perotti had been fouled in the box.
But Roma's hopes of a comeback were dashed soon after, as Falque's 20-yard effort deflected wickedly off a defender and over the unfortunated Wojciech Szczesny.
Luciano Spalletti made three changes from the side that beat Crotone in midweek - reverting to the same XI that took the field in the club's last away game, the defeat to Fiorentina seven days ago.
Daniele De Rossi came back into midfield alongside Kevin Strootman - and also reclaimed the captaincy - while Diego Perotti and Radja Nainggolan also came back in ahead of Francesco Totti and Stephan El Shaarawy.
The back four remained unchanged for the third game in a row - indicating a certain consistency at the back for the Giallorossi.
4’ – Fazio finds Dzeko over the top, but Hart comes out well to intercept.
4’ – So close! Nainggolan goes for goal from 25 yards but narrowly misses the target
8’ – Goal! Belotti meets Obi’s deep cross and buries his header. 1-0 Torino.
11’ – Dzeko scuffs wide from close range, not long after Salah had wriggled free inside the box and forced a corner
13’ – Post! Falque takes Belotti’s lay-off and hits the far post, before Szczesny does brilliantly to block the follow-up from the same player!
28’ – Dzeko first-time effort forces good save from Hart.
33’ – Peres shoots at Hart from distance, but it's easy for the goalkeeper.
35’ – Dzeko heads wide from a deep cross that left him a lot of work to do.
41' - The hosts break away and Belotti fires a powerful shot that forces another good save from Szczesny.
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47’ – Boye’s speculative effort is never testing Szczesny
50' – Great save! Dzeko rises highest to meet Perotti's cross - but Hart gets a strong palm to it and turns the ball away!
51’ – Florenzi makes an important interception to stop Baselli having an easy shot
52’ – Penalty for Torino. Belotti cuts inside Peres and goes down.
53’ – Goal. Iago Falque converts the penalty. 2-0 Torino.
54’ – Penalty for Roma! De Silvestri brings down Perotti inside the box!
55’ – GOAL! Totti converts the penalty with aplomb! 2-1.
63’ – Chance! Fazio finds Dzeko over the top again, but the striker fails to hit the target
65’ – Belotti flashes over from 20 yards.
66’ – Goal. Iago Falque’s first-time shot deflects over the helpless Szczesny. 3-1.
72’ – Peres scrambles into the box but his low drive is claimed by Hart
80’ – Martinez flashes wide from an acute angle
80’ – Totti misses the target from inside the box after a good run from Salah.
82’ – Zappacosta’s first-time effort forces a save from Szczesny.
88' - Dzeko heads wide
90' - Salah hits one into the side-netting.
90' - Szczesny saves well from Martinez once again.
See more match statistics in our match centre.
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“A negative performance and a negative result. It was a very bad day for us. But I think we represent a very big club, and when you represent a big club you have to turn a negative moment into a positive very quickly."
- Wojciech Szczesny
"We were probably missing a bit of determination. We messed up a few chances at the beginning and had these chances been better exploited, we definitely could have directed the contest in a different direction. On the contrary, when we let them in for their first chance of the game, Torino scored.
- Luciano Spalletti
Roma's next game is in Europe, as they return to the (real) Stadio Olimpico to host Romanian champions Astra Giurgiu in the second match of the Europa League group stages on Thursday.
Their next Serie A game is a big one: they host Frank de Boer's Inter Milan at the Stadio Olimpico on Sunday.
Goalscorers: Belotti (8'), Falque (53', 65'); Totti (55' p.)
Torino: Hart; De Silvestri (Zappacosta), Rossettini, Castan, Barreca; Benassi, Valdifiori, Obi (Baselli); Boye, Belotti, Falque (Martinez).
Roma: Szczesny; Florenzi, Manolas, Fazio, Peres; Strootman, De Rossi (Totti); Salah, Nainggolan (El Shaarawy), Perotti (Paredes); Dzeko.
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