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Jose Mourinho's side started slowly and went behind, leaving them chasing matters for much of the game. The Giallorossi dominated large swathes of the contest and created countless opportunities, but nevertheless found themselves unable to find a late equaliser.
Sergej Milinkovic-Savic and Pedro notched inside the opening 19 minutes to give the day's nominal host side a significant early advantage, although Roger Ibanez's header just before the half-time whistle gave Mourinho's men hope of a second half comeback.
That hope seemed to have faded when Felipe Anderson made it 3-1, only for Jordan Veretout to convert from the penalty spot minutes later to set up a frantic final 20 minutes.
Roma pushed and probed but Lazio goalkeeper Pepe Reina proved equal to everything thrown at him, as Maurizio Sarri's side held on.
Roma are back in action on Thursday night as they travel to face Zorya Luhansk in the Europa Conference League.
Their next Serie A meeting is against Empoli on Sunday.
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