Chelsea, who entered the match on the back of wins against Swansea City and Liverpool, flexed their attacking muscle after the break and were simply too good for Southampton, who lost back-to-back home matches for the first time under manager Mauricio Pochettino.
After an entertaining first half, Torres broke the deadlock in the 60th minute, reacting quickly to head into an open net after a deflected Eden Hazard cross beat Southampton goalkeeper Kelvin Davis and hit the post.
Chelsea did not have a striker score an away league goal in all of 2013, but on the first day of a new year, Torres broke the drought.
Willian then scored a fine curling strike from the edge of the penalty area with 19 minutes left before fellow substitute Oscar wrapped up the win with a composed left-footed effort.
Ramires returned from suspension for Chelsea in one of six changes, as the likes of Torres, Juan Mata and Andre Schurrle also came in, while Morgan Schneiderlin and Gaston Ramirez were recalled for Southampton.
Torres started brightly, going close twice in the first three minutes, while Schurrle – making his first league start since scoring twice at Stoke City last month – fired just wide.
Southampton defender Dejan Lovren clashed heads with team-mate Jose Fonte, causing play to stop, and after the former returned, Southampton grew into the match.
Adam Lallana's close-range shot was blocked by Ashley Cole and the same defender did well to deny Jay Rodriguez when Ramirez played him through with a lofted ball.
For the second time in 12 minutes, Davis was quick off his line to deny Hazard – he did excellently to keep out Ramires earlier – and Lallana was again denied inside the penalty area by an excellent block, this time from Cesar Azpilicueta.
Ramires was a constant threat and after a charging run, he forced Davis to tip his strike over the bar, while Hazard hesitated when he should have shot in an attacking move that ended with Schurrle's effort blocked.
Lovren and Fonte had efforts blocked as Chelsea failed to clear a corner two minutes into the second half, while at the other end, Oscar was booked for simulation after a minor collision with Davis.
An excellent ball from Hazard set up Oscar – recently brought on for Mata – but after trying to round Davis in the penalty area, he left a trailing leg in and threw himself to ground.
Chelsea were turning the screw and got their reward on the hour-mark thanks to Torres' quick reaction, but Southampton substitute Rickie Lambert fired a warning shot with a close-range header at Petr Cech with 25 minutes left.
Willian linked well with fellow substitute Oscar six minutes later though, and curled an excellent strike past Davis.
And Southampton's high line was punished again when Hazard's ball over the top sent Oscar through, and he finished with aplomb eight minutes from time.
