Three goals in seven minutes before half-time laid the platform for Spurs to reach the last eight.
Pavlyuchenko scored the first before Campbell added the next two. Pavlyuchenko scored the fourth early in the second half, shortly after Damien Plessis had struck for Liverpool. Sami Hyypia scored the visitors' second.
Spurs goalkeeper Heurelho Gomes was carried off after taking a boot in the face from Philipp Degen but the injury is not serious and he could play on Saturday.
Meanwhile, the club have released initial plans for their new stadium, including a proposal to use the ground for a season while it is partially completed.
The Northumberland Development Project, which will have a consultation process with local residents before planning permission is granted, would also require the removal of two listed buildings.