The Italians were left to rue a number of missed chances in a game they dominated.
With both sides unbeaten and already through to the last 32, first place was all there was left to play for.
Lazio needed a win in order to finish ahead of the Turkish outfit in the pool.
It was the visitors that had the first chance in the seventh minute when an unmarked Florent Malouda fired a left-footed shot from 30 yards that was kept out by Lazio goalkeeper Etrit Berisha.
At the other end, Trabzonspor goalkeeper Onur Kivrak saved Felipe Anderson's long-range attempt.
Lazio continued to press forward and almost went ahead in the 40th minute when Sergio Floccari's header from Balde Keita's cross went just wide off the far post.
The hosts continued to terrorise the Trabzonspor defence and Honorato Ederson's acrobatic kick from 15 yards flew wide.
Another chance went begging for Lazio before half-time when Felipe Anderson pounced on a loose ball in the Trabzonspor area and his shot went over the bar.
Lazio picked up where they left off after the re-start and Ederson showed good strength to ride a couple of challenges before rifling in a shot from the edge of the box that went straight at the keeper.
In the 70th minute, Berisha came off his line to clear a dangerous ball directed at Paulo Henrique.
Trabzonspor defended deeply and held on Lazio's advances to earn a valuable point in Rome.