Chelsea laboured into the Champions League last 16 with a 1-1 draw at Stamford Bridge to send former finalists Atletico Madrid crashing out.
Antonio Conte’s men, who assured qualification to the knockout stages with victory over Qarabag last month, needed three points to guarantee top spot.
However, Roma clinched maximum points to ramp up the pressure on the Blues.
Saul Niguez turned in Fernando Torres’ header to fire the away side in front on 56 minutes, which was their first Champions League away goal since the Spaniard scored at Leicester City in April.
Chelsea talisman Eden Hazard sparked the equaliser. His left foot drive from the side of the penalty area was turned in by former Manchester City defender Stefan Savic.
Conte’s men couldn’t find a winner in the final 15 minutes and Roma surged through ahead of Chelsea into the last 16.
Diego Perotti’s beautiful strike was enough for the Italians to draw level with the English champions on points.
But the Rome-based side advance as group winners thanks to their superior head-to-head record.
Manchester United beat CSKA Moscow 2-1 at Old Trafford to finish top of Group A, while Swiss champions Basel won 2-0 away at Benfica to join them in going through.