Diego Simeone's men have a poor recent record against Alaves, having won just one of seven league encounters prior to this weekend's meeting.
And it looked set to be another frustrating evening for Atleti in a match of few goalscoring opportunities.
However, Torres opened his league account for the campaign five minutes after his second-half introduction to clinch three points that lift Atleti above Valencia into second in the table, extending their record unbeaten run to 20 league matches in the process.
Following Valencia's defeat to Eibar earlier in the day, Atleti now lead Marcelino's men by two points, with Barcelona – who face Deportivo La Coruna on Sunday – three clear at the summit.
Both sides struggled to create chances during a cagey opening and Ruben Duarte's optimistic strike from outside the box after 20 minutes was as close as either came - the full-back's fizzing effort was probably sneaking wide, but it had Jan Oblak scrambling to meet it.
Kevin Gameiro swung a boot at a bouncing Antoine Griezmann throughball five minutes later but failed to make contact under pressure from two Alaves defenders, before Koke had an improvised volley saved as the visitors frantically guarded their goal.
Burgui resisted the temptation to shoot when he had a clear opportunity to test Oblak five minutes from the break but, while Angel Correa's introduction for the second half gave Atleti more attacking impetus, they continued to find it difficult to punish such missed opportunities by their opponents.
Simeone passionately attempted to energise the home fans as the match ticked beyond 70 minutes with Koke's first-half volley still the best chance for either side, but a Gabi header soon after deflected harmlessly over the crossbar.
The Argentinian coach's next move was to throw on Torres and Yannick Carrasco in a bid to swing the match in his disappointing side's favour, and the former made a swift impact.
A superb Sime Vrsaljko cross from the right was perfectly placed for Torres to apply a left-footed finish from close range in the 74th minute.
With Alaves' resistance broken, the three points appeared safe for Atleti, and the visitors were short of ideas in their pursuit of an equaliser.
