Two goals from Fernando Torres and one from Raul Meireles gave Liverpool their first win since they beat Bolton Wanderers on New Year's Day and brought a huge smile to the craggy face of the Scotsman who replaced Roy Hodgson as manager on January 8.
"It was nothing short of what we deserved. We will always be competitive. We might not be smashing people across the nose with their elbows, but we'll always be competitive," Dalglish told Sky Sports after Liverpool's second away win of the season in the Premier League.
"The way we worked was great credit to them, we are one unit, there are no divisions in this football club and if we stick together we've got a chance."
Dalglish hailed Spain striker Torres's "fantastic" performance, adding: "Apart from his two goals, he worked his socks off and he was threatening most of the time, that performance will do for us."
The win lifted a far more composed Liverpool from 13th to 10th and left Wolves, despite all their battling qualities, just one point and one place above bottom club West Ham United who are away at Everton in a later kickoff.
Torres opened the scoring after 36 minutes when Christian Poulsen beat the offside trap with a pass down the right to Meireles.
The Portuguese midfielder took the ball into the Wolves area before squaring for Torres who tapped in.
Meireles, who scored his first Liverpool goal against Everton last week, doubled the lead with a spectacular 20-metre dipping volley that flew over helpless keeper Wayne Hennessey after 50 minutes.
FLOWING MOVE
Torres cracked home the third from close-range in stoppage-time to round off a long-passing move that carried the ball from one of the pitch to the other.
That move evoked memories of the Liverpool of old, when they dominated and won matches almost as a right, sweeping aside the opposition and challenging for titles.
There has been little evidence of that old authority this season, but Saturday's victory hints at better times to come under Dalglish, who guided Liverpool to their last championship in 1990 before quitting the following year.
"If you are going to come to Molineux and you don't put in a performance, there is no way you are going to get a result," Dalglish said.
"The way the lads competed is a reflection of what they have been like since we've come in, and maybe today we never looked like losing."
Liverpool's victory avenged Wolves' shock 1-0 win at Anfield last month, a result that hastened the departure of Hodgson and the return of Dalglish.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
