Tesche struck after 42 minutes in a low-grade contest befitting its status with neither side able to go up or be relegated.
The corresponding fixture last October marked Neil Lennon's first game in charge after replacing Dougie Freedman.
Lennon was sent off as Wanderers won at St Andrews but the Ulsterman saw nothing from his team on this occasion to raise the blood pressure.
And he, rather than rival boss Gary Rowett, was grateful to bring the curtain down on the campaign.
It may have been a meaningless match but Blues marked the occasion by bringing 3,616 fans, many decked out in fancy dress.
There were certainly none of the nerves for the away supporters as there were in last season's corresponding fixture.
Two-nil down with 12 minutes left, the Blues - under Lee Clark - saved their Championship status with goals from Nikola Zigic and Paul Caddis.
This time there was nothing resting on the outcome and it showed. Veteran Eidur Gudjohnsen went closest early on for Wanderers with a free-kick saved by Darren Randolph.
Tesche tested Adam Bogdan but the Hungarian international, in what could have been his final game for the club, also dealt with the danger.
Definitely leaving the Macron Stadium is Scottish international Barry Bannan. And he marked his final game before his return to Crystal Palace with a booking for bringing down Blues' man in the mask, Diego Fabbrini.
With Gudjohnsen, Bolton's skipper for the day, linking play superbly, Mark Davies was able to try his luck from 18 yards only to see the ball drift wide.
Ex-Blue Emile Heskey headed narrowly wide from Adam Le Fondre's neat cross from the right as the Trotters tried to finish the first half in the ascendancy
Instead, it was Blues who took the initiative before the break. Firstly Jonathan Grounds went close with a right-foot curler after being set up by Lloyd Dyer.
And three minutes before the break Blues did take the lead with a soft goal as far as Bolton were concerned.
Demarai Gray's in-swinging corner was missed by Dean Moxey and Wanderers' player of the year, Tim Ream. Bogdan cleared the ball off his own goal line only for Tesche to drive the rebound into the net.
Wanderers lookled more lively at the start of the second period and Gudjohnsen had a goal disallowed for offside. The former Chelsea and Barcelona striker had another effort charged down by Grounds
Blues survived and looked to double their advantage through Fabbrini's shot while Gray went closer as he cut in from the left.
In the end, they comfortably saw out the rest of the game as Wanderers finished their season with just one win from their nine remaining games.