The home side took the lead in the 11th minute when Paulo Henrique found Yusuf Erdogan with room inside the penalty area, allowing the winger to slot under Federico Marchetti to put Trabzonspor 1-0 ahead.
Lazio gave themselves a lifeline in the 30th minute following a good passing move which found Ogenyi Onazi in the box, with the striker taking his time to apply a composed finish into the bottom corner.
However, Trabzonspor restored their two-goal lead when Henrique took full advantage of some efficient passing to smash home from close range and put his side 3-1 up before half time.
Lazio applied pressure following the break as they tried to get back into the game as Hernanes met a cross, but his header went straight into the hands of the home goalkeeper.
It looked as though Trabzonspor's two-goal lead would be enough, but for Sergio Floccari who produced two goals in the space of a minute to earn Lazio an unlikely draw in the final stages of the game.