Besiktas leapfrogged us into first place and both teams progress into the knockout stage of the competition. The draw for the Round of 32 is on Monday.
Tosun's winner came against the run of play on the hour and just seconds after the same player had rattled the woodwork.
We responded well immediately after the goal but Roberto Soldado saw one goal-bound effort blocked and another deflected just wide - that just about summed up our night.
Play was also suspended twice as the floodlights failed on two occasions at the Ataturk Olympic Stadium - the first led to a 15-minute delay in the first half, the second a delay of approximately 12 minutes in second half added time.
There were changes across the team with returns for Danny Rose, Younes Kaboul, Paulinho, Andros Townsend, Mousa Dembele, Nacer Chadli and Benjamin Stambouli, plus an outing for Michel Vorm and a welcome comeback for Kyle Walker.
There was nearly an opening 10 minutes in when Dembele set Townsend scampering down the left and the England man dispatched a cross that was just a little too high for the leap of Soldado.
Two minutes later the lights went out and the noise levels increased from the home support, but the teams left the pitch and the music began.
As play resumed, Chadli released a shot that did not trouble Tolga Zengin in the home goal as the game struggled to ignite as before the interruption, but Soldado should have scored when Kaboul headed back in his direction inside the six-yard box from Paulinho's free-kick, but Zegin fielded again.
The ball went in via Chadli after the tempo of the game began to be dictated totally by the team in yellow. Unfortunately, the ball landing in the net was accompanied by the raising of the flag by the referee's assistant.
Soldado broke inside the area and was literally a fraction from finding Paulinho with a perfect ball, but the shin of a defender rescued the home side.
The first 10 minutes of the second half continued in much the same fashion as the first, with the team dictating possession without really threatening.
The course of the game changed, however, just before the hour when Tosun tapped in after being set up by Olcay Sahan. Tosun fired a warning shot against the crossbar moments earlier.
It sparked joy amongst the already raucous crowd and showed the need to be more clinical in front of goal and capitalise on possession - which was plentiful for the team.
Soldado was unlucky with a volley from a Paulinho corner that was deflected just wide before Rose fired into the arms of Zengin from 20 yards.
Kerim Koyunlu could have doubled the lead when put through on 67 minutes, only to shoot into the side netting, while we prepared a double change with the introduction of Erik Lamela and Aaron Lennon.
Soldado and Paulinho made way, with Chadli pushed up highest in a striking role. Etienne Capoue came on for Walker with 15 minutes remaining, with Stambouli nominally operating from the right while not in possession.
It was Besiktas who appeared to take more of the initiative following the changes, with no real threat being applied to the home goal, and with Slaven Bilic's men looking potent on the break as the game stretched.
We were camped in Besiktas' half in the final minutes - including after the second break for floodlight failure - but couldn't carve out the chance needed.
Besiktas: Zengin (C), Kurtulus, Sosa, Tore (Koybasi, 84), Sahan, Franco, Uysal, Koyunlu (Yaman, 90+2), Gulum (Nukan, 46), Tosun, Motta. Substitutes (not used): Metin (GK), Karaal, Kaya.
Spurs: Vorm; Walker (Capoue, 76), Chiriches, Kaboul, Rose; Dembele, Stambouli; Townsend, Paulinho (Lennon, 69), Chadli; Soldado (Lamela, 69). Substitutes (not used): Lloris, Davies, Fazio, Onomah.
Goals: Besiktas - Tosun (60).
Referee: Stefan Johannesson (Sweden).