With Milan, Napoli and Juventus all earning three points this weekend, champions Inter fell behind early on in Turin as they looked to keep pace, with Torino's Brazilian defender Bremer stabbing home the ball with 12 minutes on the clock.
Chances came and went for Inter in the second half, with Edin Dzeko heading over the most glaring opportunity from a glorious position late on as the visitors' moment seemed to have come and gone.
Substitute Sanchez's composure in the 93rd minute, however, snatched what could be a crucial point for Inter in their quest to retain the Scudetto.
Simone Inzaghi's third-placed side are four points behind leaders AC Milan with a game in hand, with Juventus only three points further back. Torino stay 11th.
"To win the Scudetto, we need to approach matches better," Inzaghi told DAZN.
"We lost energy and players through injury at crucial moments of the season, but this shouldn't be an excuse. We have 10 'finals' plus the Italian Cup to come.
"Now we need to recover energy and some results. There is physical and mental fatigue, but we are Inter and we have to do better."
An impressive win at Liverpool in the Champions League in midweek, following a 5-0 thrashing of Salernitana last weekend, gave fans hope that Inter had turned the corner after recent poor form, but Bremer's opener heightened fears that a title defence may be beyond them.
Other than Lautaro Martinez's header that was well saved, Inter did not look like scoring in the first half, but the visitors stepped it up after the break with substitute Federico Dimarco denied by a fine stop by Torino goalkeeper Etrit Berisha.
Dzeko then headed wide from a good position, before Torino had two chances to double their lead, with Josip Brekalo firing over and Inter goalkeeper Samir Handanovic denying Tommaso Pobega with a stunning save.
After veteran Bosnian striker Dzeko had somehow missed the target again with a header, Inzaghi sank to his knees, frustrated at an opportunity missed.
Sanchez's fine finish - his first goal since early February - salvaged a point moments later but, against a Torino side without a win in six league games coming into the contest, Inter may look at this result as two points dropped.