Second half goals from Alan Shearer (2) and Craig Bellamy were enough to seal a comfortable 7-1 aggregate win for The Magpies.
Newcastle will now face PSV Eindhoven in the last eight as they keep their hopes alive of winning silverware this season.
Newcastle started brightly and Laurent Robert tried his luck with a free kick from fully 40 yards which Mallorca keeper Miki unconvincingly pushed out.
The Magpies went close to putting the game beyond Mallorca on nine minutes when Jermaine Jenas won the ball off Marcos and skipped past Federico Lussenhoff on the edge of the box and fired in a shot which Miki just about tipped round the post.
Mallorca started to get a foothold in the contest and they almost broke the deadlock on 13 minutes with the first noteworthy chance of the game when Arnold Bruggink swapped passes with Jesus Perera and curled a shot towards the top corner which Shay Given did well to tip over the crossbar.
Despite making so many changes to the side Mallorca were beginning to gain more confidence as the game wore on and Bruggink had another two efforts which Given saved easily.
Newcastle seemed content to sit on their lead inviting Mallorca onto them and Anderson Nene fired in a shot from the edge of the area on 35 minutes which Given could only gather at the second attempt.
The home side missed the best chance of the first half five minutes before the break when substitute Alejandro Campano broke free down the right and crossed for the unmarked Toni Gonzalez inside the box, but under pressure from Given he fired his shot just past the post.
Newcastle made a dream start to the second half with Shearer breaking the deadlock seconds after the restart following a mistake by Miki.
Miki miskicked a clearance straight to Shearer 30 yards out and the former England captain controlled the ball before firing it back past the diving Miki for his 23rd goal of the season.
Mallorca refused to bow down and only a magnificent save from Given prevented Nene from drawing them level on 56 minutes as the Republic of Ireland goalkeeper somehow got his legs to a deflected shot from Nene.
Given denied the same player again three minutes later with another fine save as Mallorca tried to make the scoreline respectable.
Newcastle were looking dangerous on the break as Mallorca threw numbers forward and Jenas nodded Gary Speed's cross just over the crossbar.
Substitute Hugo Viana almost got clear on goal 12 minutes from time, but Miki was quickly off his line to clear the danger with his legs as the Portuguese star tried to go round him.
Newcastle did add to their lead on 78 minutes with substitute Bellamy scoring just a minute after coming off the bench.
Newcastle caught Mallorca on the break as Bellamy picked up the ball inside his own half before racing clear from the home side's defence before brilliantly chipping Miki with a neat left-footed effort.
Newcastle added to Mallorca's misery in the final minute when Olivier Bernard unselfishly squared the ball for Shearer across the six-yard box to tap home his second goal of the night and seal a good night's work for Sir Bobby Robson's men.
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