The £13.8million Russia international, who was starting after hitting a double as a substitute against Wigan at the weekend, put Spurs ahead after 23 minutes with a tenacious turn and finish.
Tottenham's passage was sealed with own goals either side of half-time from Bolton goalkeeper Jussi Jaaskelainen and defender Andy O'Brien.
Pavlyuchenko then rounded off the evening with the fourth, which he slotted past Jaaskelainen after being picked out in the box by substitute Danny Rose.
Pavlyuchenko, who was making his first Tottenham start since October 27, replaced Peter Crouch up front and will have given manager Harry Redknapp plenty of food for thought. He could have a major role to play now as Tottenham bid for a top-four finish and FA Cup glory.
Bolton boss Owen Coyle also has plenty to think about, and the former Burnley manager must be worried for his team's form after another defeat.
Spurs started at a vibrant tempo and Pavlyuchenko was involved early, attempting a Dennis Bergkamp-esque turn in the box.
Jermain Defoe then linked with David Bentley down the right but Jlloyd Samuel was on hand to clear the low cross and Bolton survived the initial onslaught.
Bolton were sitting deep, allowing Sebastien Bassong time to carry the ball unchallenged from halfway before unleashing a fierce drive from 30 yards which flew just wide.
David Bentley snuffed out a promising left-wing run from Samuel and Ricardo Gardner was lively in possession for Bolton but it was Tottenham who were making all the running.
Gareth Bale surged down the left wing, swung over a ball to Bentley who teed up Bassong again but his fierce effort was blocked.
Wales international Bale then gifted the ball to Klasnic.
The Bolton striker's rifled shot had Heurelho Gomes at full stretch but it flew just wide of the goalkeeper's right post.
Bolton then worked the best early chance of the game when Sam Ricketts spotted Gardner unmarked at the far post but his cross was just too high and curled out of play.
And having survived at one end, Spurs marched downfield and immediately took the lead through Pavlyuchenko.
Luka Modric slid a pass to the edge of the box where Pavlyuchenko turned Zat Knight and slid the ball past Jaaskelainen and inside the far post.
Spurs piled forward again and Defoe cut infield, away from O'Brien before unleashing a dipping shot which Jaaskelainen did brilliantly to push behind for a corner with a diving save.
But just minutes later the Bolton goalkeeper undid all his good work with a bizarre own goal as Tottenham took control of the tie.
Defoe launched himself at a low, driven cross but Jaaskelainen got there first and deflected the ball into his own net off the inside of his right leg.
Gomes preserved the two-goal lead with a smart low save from Klasnic.
The second half was only two minutes old when Spurs took a 3-0 lead following another defensive howler from Bolton.
O'Brien slid in to meet Bale's left-wing cross at the near post but succeeded only in deflecting it past the helpless Jaaskelainen.
Pavlyuchenko then tested Jaaskelainen with a turn and strike from the edge of the box but the Bolton goalkeeper caught it at the second attempt.
Eidur Gudjohnsen, a half-time replacement for Defoe, thought he had extended Spurs' lead further but his strike was ruled offside.
Pavlyuchenko wrapped up the victory with his second goal of the evening and sixth of the season.
Rose played the ball into the heart of the box and Pavlyuchenko's deft touch took him away from Knight before he slotted past Jaaskelainen.