Yet, after De Rossi went off injured, Porto regained control and were back in front seven minutes after the break.
Porto's persistence eventually paid off in the 26th minute as Moussa Marega combined with Tiquinho, who slotted home from close range to make it 2-2 on aggregate.
Telles took responsibility and made no mistake from 12-yards out to seal a 3-1 win on the night and a 4-3 win on aggregate.
The decisive goal came in the 117th minute, when Alex Telles scored from the penalty spot after Alessandro Florenzi was judged to have pulled Fernando's shirt following a VAR review. The first leg ended 2-1 in favour of the Serie A side.
But the noise around his future at the club has reached a crescendo after Roma were knocked out of the Champions League in the last 16 stage at the hands of FC Porto.
Porto captain Hector Herrera, who was booked and will miss the quarter-final first leg, tested Robin Olsen with a bending effort just before the break when Roma lost skipper De Rossi following a crunching tackle by Danilo.
Marega is now level with Lionel Messi and Dusan Tadic with six goals in this season's tournament. Both matches can be streamed via fuboTV (Try for free).
With penalties seemingly on the horizon, Porto grabbed a dramatic victor after Turkish referee Cuneyt Cakir pointed to the spot, after reviewing an incident in which Florenzi hauled back Fernando as the substitute stretched to reach a driven low cross.