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."
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.
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.
