Maxi Rodriguez and Martin Kelly both scored in a five-minute spell after the break to maintain Dalglish's unbeaten record against Chelsea in 13 matches as Liverpool manager.
Liverpool's win was fully deserved, even with the inspirational Luis Suarez rested, as they were able to recover from the setback of Andy Carroll's missed first-half penalty to secure their third straight victory at Stamford Bridge.
It was a fully deserved win, following hard on the heels of the Premier League triumph here ten days ago and confirming a renaissance that has seen Liverpool go undefeated in their last eleven games.
And as his side closed in on the semi-final, Dalglish showed special appreciation for the contribution of Craig Bellamy when he was substituted late on.
He was withdrawn from Sunday's game against Manchester City at Anfield following the death of his mentor and Wales manager Gary Speed, but returned in style at Stamford Bridge to create both goals.
Liverpool can now contemplate their first semi-final in this competition since 2005, when they reached the final only to be defeated by Jose Mourinho's Chelsea.
In contrast to Dalglish's obvious delight, Villas-Boas cut a dejected figure as the momentum built by the victory against Wolves on Saturday was snuffed out by an impressive Liverpool display.
The 34-year-old Portuguese coach insists he has the full backing of Chelsea owner Roman Abramovich and there is no doubt he is currently presiding over a squad in need of major repair.
But this result only makes next Tuesday's defining Champions League meeting with Valencia at Stamford Bridge an even more crucial moment for Villas-Boas, despite his managerial career at Chelsea being in its infancy.
And it was another disappointing night for Chelsea's £50m British record signing Fernando Torres, who cut an almost apologetic figure against his former club as he laboured in vain on the margins.
Carroll and Torres were both given chances to impress as both managers made changes - but it was referee Phil Dowd who was the central figure early on as he ignored two penalty appeals.
He booked David Luiz for diving when he was clearly felled by Sebastian Coates as he raced into the area - but the Chelsea defender was then lucky to escape punishment for a push on Carroll.
Dowd did award a penalty, albeit after a lengthy delay, at the third time of asking in the 22nd minute when Alex handled needlessly. Carroll claimed the penalty with some confidence only to drill it straight at Chelsea keeper Ross Turnbull.
The official was not enjoying his finest night, as he proved when he booked Ryan Bertrand for a dangerous tackle on Jordan Henderson - by Romelu Lukaku.
Chelsea at least posed a whiff of danger early in the second half when Florent Malouda's downward header looped up on to the bar, but this was only the signal for Liverpool to put the game out of their reach.
Liverpool went ahead just before the hour when Bellamy broke clear down the right and crossed perfectly for Maxi, who also scored in the recent league win at Chelsea, to beat Turnbull comfortably at the far post.
Villas-Boas immediately prepared the introduction of Juan Mata and Nicolas Anelka, but he was not able to make the change before Liverpool extended their lead.
Bellamy's free-kick found Kelly unmarked in the area and the defender took advantage to head past the exposed Turnbull.
Mata and Anelka came on, but Liverpool cruised to victory untroubled to move a step closer to Wembley.