The £50million man, like Brazilian defender David Luiz, did not complete his move to Stamford Bridge in time to be available for Tuesday evening's game at the Stadium of Light, but he was not missed as the Blues created more than enough chances to win the game without him.
In the end, Anelka's nonchalant injury-time finish and skipper John Terry's strike on the hour were the difference between the sides, but the visitors hit the woodwork three times, twice with the same Salomon Kalou shot, and were repeatedly kept out by Craig Gordon on their way to a second successive Premier League win on the road.
Sunderland had taken an early lead through Phil Bardsley and after Frank Lampard's penalty and Kalou's 23rd-minute strike had restored order, Kieran Richardson levelled before the break.
But Carlo Ancelotti's men, who started and finished the night 10 points adrift of leaders Manchester United, were good value for a victory which gained a measure of revenge for their 3-0 home defeat by the Black Cats in November.
Stephane Sessegnon enjoyed a promising debut for the home side with Sulley Muntari watching from the stands, but a crowd of 37,855 left knowing the points had ended up with the better side on the night.
The Blues arrived on Wearside having invested a British record transfer fee in Torres late last night as the January merry-go-round almost span off its axis, but it was not lack of firepower which was manager Carlo Ancelotti's concern during the opening 45 minutes.
The Italian saw his side score twice and once upon a time in the not so very distant past, that was more than enough for Chelsea to claim all three points.
However, the Londoners not only handed their hosts an early lead, but also gifted them a way back into the game with the kind of lax defending which perhaps prompted another big-money move for Benfica's Luiz.
The game was only four minutes old when makeshift Sunderland left-back Bardsley picked up possession on halfway and with nobody closing him down, made his way towards goal.
As he approached the penalty area, he cut inside John Obi Mikel and with few obstacles in his path, sent a swerving right-foot shot past the flat-footed Petr Cech and into the bottom corner.
The home fans sensed a repeat of the stunning 3-0 win at Stamford Bridge in November, but Chelsea flexed their muscles and were level within 11 minutes.
Quite what Ahmed Elmohamady was trying to do when he climbed all over Ashley Cole as the pair fought for Michael Essien's teasing cross may remain known only to him, but referee Mark Halsey had little choice but to point to the spot and Lampard needed no second invitation.
Chelsea sensed an opportunity as Terry made the most of the freedom afforded him by the Black Cats' one-man frontline, and they went ahead eight minutes later.
Anelka pounced on a loose ball to slide Kalou in, and the Ivory Coast international deftly tucked a shot past the advancing Gordon.
Despite the best efforts of both managers, the game remained dangerously open, but it was Sunderland who struck the next blow when, after Elmohamady had been felled by Mikel, Richardson sent a free-kick through a crumbling wall and into the back of the net.
Branislav Ivanovic hit the crossbar and Didier Drogba headed straight at Gordon in a whirlwind finish to the half, and even the spectators were glad of the break by the time the whistle sounded.
Chelsea returned in similarly determined mood and it took a fine block by Nedum Onuoha to deny Lampard a second and yet more determined defence to prevent either Anelka or Kalou from bundling Ivanovic's flick-on home.
But they regained the lead on the hour when, after Gordon had pulled off a fine save to keep out Lampard's powerfully-struck effort, Terry hit the rebound into the ground and saw it arc over the keeper and into the net.
Gordon was relieved to see Kalou's 67th-minute shot hit both posts and run to safety after Anelka had carved the Black Cats wide open with Sunderland hanging on for dear life.
They reached five minutes of stoppage time still only one goal in deficit, but their late heroics against Newcastle were not to be repeated as Anelka instead struck at the death to seal an impressive victory.