Dybala returned from a knee injury sustained in the first-leg 1-1 draw a week ago in Portugal, and Roma advanced on a 4-3 aggregate score on Thursday.
Porto went ahead thanks to Samu's acrobatic volley over his shoulder to take a 2-1 aggregate lead, but Dybala started the comeback with an equaliser in the 35th with a left-footed shot inside the far post. The second clinical finish came from inside the area to the near post.
Porto's hopes were dented when Stephen Eustáquio was sent off after getting a red card only six minutes into the second half.
Substitute Niccolò Pisilli added the third before another substitute Devyne Rensch's own goal in stoppage time.
Roma, the 2022 Conference League champions, next play either Lazio or Bilbao.
Alkmaar advanced after a 2-2 draw with Galatasaray that saw the Dutch club reach the next round on a 6-3 aggregate score.
Alkmaar got goals from Seiya Maikuma and Denso Kasius before Victor Osimhen struck for the Istanbul club. Roland Sallai's equaliser salvaged at least a draw on the night for the hosts.
Alkmaar are set to face either Manchester United or Ange Postecoglou's Tottenham next.
Romanian team FCSB beat PAOK 2-0 to progress on a 4-1 aggregate score.
Norway's Bodø/Glimt scored twice in extra time to beat Dutch side Twente 5-2 on the night and 6-4 on aggregate.
Three goals in stoppage time sent the match to extra time where goals from substitute Sondre Brunstad Fet (111th) and an own from Arno Verschueren (114th) confirmed the win.
The Norwegian team is amid a winter break that will not end until the start of the domestic league on March 29.
Real Sociedad beat Midtylland 5-2 to progress 7-3 on aggregate, while Viktoria Plzen defeated Ferencvaros 3-0 for a 3-1 victory overall.
Jose Mourinho's Fenerbahce drew 2-2 with Anderlecht away to advance 5-2, while 10-man Ajax converted an all-important 93rd-minute penalty in extra time from Kenneth Taylor to go down 2-1 at home to Union Saint-Gilloise (Kevin Mac Allister 16th, Promise Akinpelu 28th).
The result was enough to see Ajax squeeze past Union 3-2 on aggregate.
In other action involving some of the bigger-name teams in the third-tier Conference League, Real Betis were reduced to 10 men eight minutes before time and conceded a winning goal from Gent but still advanced thanks to their 3-0 victory in the first leg.
Copenhagen edged Heidenheim 3-1 in extra time to make the next round 4-3 on aggregate, while Panathinakos beat Vikingur Reykjavik 2-0 for a 3-2 victory in the tie.
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