Goals from Yusuf Erdogan and Adrian Mierzejewski gave the hosts a 2-0 lead midway through the first half and after Ogenyi Onazi reduced the deficit for Lazio, Trabzonspor struck again before half-time through Paulo Henrique.
Floccari, though, then came to the rescue with two goals for the visitors and the result leaves Lazio and Trabzonspor level on four points at the top of the pool.
The Turkish outfit went into the encounter riding a three-match winning streak in the Super Lig and were on the attack from the off.
They took a 12th-minute lead when a fast counter-attack saw Yusuf Erdogan surge inside the area and strike a right-footed shot past Lazio goalkeeper Federico Marchetti.
Ten minutes later and Marchetti could do nothing to prevent Trabzonspor's second of the evening as Mierzejewski's powerful strike from 30 yards took a deflection off Lorik Cana and ended up in the back of the net.
Lazio reacted and pulled one back when Brayan Perea fed Onazi in the box and his strike beat Trabzonspor goalkeeper Onur Kivrak.
The Italians shot themselves in the foot in the 34th minute as they failed to clear a dangerous ball in the area, leaving Paulo Henrique to connect with Mierzejewski's pass and hit a right-footed shot past Marchetti.
Lazio showed more determination after the restart and had Felipe Anderson and Floccari's goal-bound attempts kept out by Kivrak.
Their efforts paid off in the 84th minute when Kivrak came off his line to clear a corner only to see Floccari anticipate him and head the ball into the back of the net.
And a minute later Floccari equalised when he was set up by Perea in the box and his 12-yard strike beat Kivrak.