The Portuguese club, who reigned supreme in 1961 and 1962, will start as favourites for the second leg after late goals from Spanish midfielder Nolito and Argentine Nicolas Gaitan (pictured) left Trabzonspor facing an uphill task.
There were also first leg wins for Croatian champions Dinamo Zagreb, FC Copenhagen, Czech's Viktoria Plzen and Israel's Maccabi Haifa.
"My team pleasantly surprised me today, we were physically stronger than Trabzonspor in the second half," said Benfica coach Jorge Jesus.
"The first goal was key, we played with a lot of experience and Nolito came in fresh at a time when Trabzonspor were giving away more space."
Dinamo Zagreb will also approach their second leg next week full of confidence thanks to a 2-1 victory in Finland against HJK Helsinki achieved with a late goal by Brazilian Sammir.
Dinamo, who have not reached the Champions League group stage since 1999, went behind when Alexander Ring fired the hosts ahead with a superb 15th-minute lob.
The visitors equalised four minutes later with a comical own-goal by Brazilian defender Rafinha who miscued an attempted clearance straight past his helpless keeper.
Shamrock Rovers kept alive their dream of becoming the first Irish team to reach the Champions League's group stages as a 1-0 away defeat in Copenhagen, who reached the round of 16 last season, set up a lively second leg in Dublin.
Denmark's other representatives in the round, Odense BK, drew 1-1 at home to Greek club Panathinaikos - Tore Reginiussen equalising for the hosts in the last minute.
Plzen, playing in the Champions League qualifying rounds for the first time, had Vaclav Pilar to thank for a 1-0 victory away to Norwegian side Rosenborg.
Haifa edged a narrow 2-1 home win against Maribor while Belgium's Standard Liege drew 1-1 at home to FC Zurich after Nacho Gonzalez came off the bench to equalise in the 90th minute after Admir Mehmedi put the Swiss side ahead.
The third qualifying round winners are battling for a spot in the playoff matches where they could seal a berth in the lucrative group phase.
