Having seen improvements on the pitch if not in results in his three previous matches in charge after taking over from Roy Hodgson the Scot finally got the victory he was craving.
Torres scored his eighth and ninth Premier League goals of the season either side of Raul Meireles capping a fine individual performance with a brilliantly-taken second-half volley.
It was only Liverpool's third away win in the league in 13 months and their first point outside Anfield since the 1-1 draw at Wigan on November 10.
The result does not paper over the obvious deficiencies in the squad - which Dalglish is trying to rectify with moves for Ajax forward Luis Suarez and Blackpool midfielder Charlie Adam - but reinforces the belief among the current players given to them by the appointment of the club legend.
Such has been the 59-year-old's influence he is even starting to get performances out of players who have failed to live up to their potential, with Christian Poulsen and Meireles in particular displaying that in this game.
Meireles, playing in the attacking midfield role given to him by Dalglish in the absence of Steven Gerrard, serving the final game of a three-match suspension, has now scored in his last two matches and his form presents his manager with a conundrum for the midweek visit of Fulham when the captain will be available again.
Poulsen's restoration to the starting line-up began badly with a fourth-minute booking but his day was to improve with the defence-splitting pass which created the goal.
It was a rare moment of quality in a first half which was spoiled partly by the poor state of the pitch and partly by the teams, neither of whom really got into their rhythm.
The Denmark international is intrinsically associated with Roy Hodgson's six-month reign of failure at Anfield but Dalglish believes he has more to offer - which is more than can be said for the former Fulham boss's other maligned signing Paul Konchesky who failed to make the squad.
Poulsen's repertoire is not renowned for having many creative interventions but the pass he picked out Meireles with was perfectly-executed through the inside-right channel.
The Portugal midfielder, played onside by full-back Ronald Zubar on the other side of the pitch, seized on the opportunity and raced into the penalty area before cutting the ball back to Torres who side-footed home one of his most straightforward chances of the season.
Meireles had a decent half without being dominant, certainly in the physical midfield battle with Wolves, but showed his class prior to setting up the goal with a brilliant 40-yard diagonal pass to pick out Torres only for the striker to cut inside and shoot straight at Wayne Hennessey.
He also flashed a half-volley wide of the goalkeeper's right-hand post as he continued his improvement in the advanced midfield role he prefers.
Wolves' two best efforts of the first half were Kevin Doyle's mis-hit cross from wide on the right which almost caught out Jose Reina, who did well to smother Steven Fletcher's close-range shot at the far post in added time.
Dirk Kuyt should have doubled the advantage early in the second half when put through one-on-one by Maxi Rodriguez but he delayed his shot and Hennessey charged out to block.
The Wolves goalkeeper was powerless, however, to do anything about the second when it came in the 50th minute.
Daniel Agger's long punt forward was only partially headed clear by Christophe Berra, under pressure from Kuyt, and Meireles lashed a brilliant dipping 25-yard volley inside Hennessey's left-hand post.
The Portugal international had been threatening to do something similar all season and the confidence from his maiden Liverpool goal in last weekend's Merseyside derby showed in the quality of that right-footed strike.
Wolves responded with a brief spell of pressure but although Liverpool have the league's worst record for squandering points from winning positions they held out.
Jonjo Shelvey, on as a substitute for Poulsen, should have put the game beyond doubt with only his second touch - his first having set up his chance from Meireles' pass - but blazed wide with only Hennessey to beat.
Torres continued to pose a threat on the counter-attack and in added time fired into the roof of the net after Kuyt's strong run into the area.
Victory has Liverpool looking up the table with more optimism under Dalglish than they had under Hodgson.