Despite both clubs failing to beat Romanian side CFJ Cluj earlier in the competition, this was deemed to be the battle of the best sides Group A has to offer, but a dull match failed to ignite until Terry's late intervention.
Neither side looked entirely convincing in a tight first half full of niggling tackles and half-chances.
Frank Lampard had the best of Chelsea's attempts, firstly pouncing on a bouncing ball in the ninth minute and striking a dipping volley that was saved by Roma keeper Doni away to his left.
Then, on 22 minutes, Philippe Mexes was booked for a foul on John Obi Mikel just outside the Roma box and, from the resulting free-kick, Lampard rifled a shot that looked destined for the top right-hand corner of Doni's goal only for his effort to clip the bar.
Most of Chelsea's best chances came through the centre of midfield as, despite the efforts of Salomon Kalou on the right, Nicolas Anelka as the sole striker only came into the game when Lampard and Deco gave him support.
By half-time Chelsea manager Luiz Felipe Scolari might have been left ruing his decision to play with a lone frontman as the French forward struggled to involve others in the game.
Roma never came close to capitalising on Chelsea's inadequacies in attack though, with captain Francesco Totti quiet except for one moment of brilliance 36 minutes in which almost provided Matteo Brighi with a clean shot on goal.
Instead it was left to the second half to provide the only goal of the game, but not before last year's Champions League finalists had laid a second-half siege on the Roma goal.
After 15 minutes of football played almost entirely in the Italian club's half, a Lampard free-kick found the unmarked Kalou whose header was straight at Doni, who parried the ball away.
That was the only action Doni saw, except for watching as his defence scrambled away a number of Lampard set-pieces, before picking the ball out of his net in the 77th minute.
The England international took what proved to be the decisive corner, swinging a cross into the near post where Terry rose bravely to flick the ball into the far corner of the net.
Chelsea played out the remaining 13 minutes without too much trouble. In fact Roma's only shot was a ridiculous Mexes effort from fully 45 yards, as the gritty Italians proved unable to perform as well in attack as they had in defence.