The battle of unbeaten boxers had challenger Kovalev pegged as the favourite by many, and he showed exactly why after taking the initiative in the first two rounds before dropping Cleverly twice in the third.
Cleverly was saved by the bell at the end of that round, but the Russian stormed immediately out of the blocks to finish what he started in round four and complete his 20th knockout victory in 23 fights.
The defeated Welshman appeared to be finding his way into the bout with good movement and a solid jab until he left his guard down for a killer head shot, before a torrent of abuse to the body led to the two knockdowns in the third, although he somehow avoided defeat there and then.
He was clearly in no condition to rally back even after a minute in the corner, however, and 'Krusher' Kovalev picked him off to collect his first world title - the first of many, according to the fast-rising star.
"This is the first world title for my collection," Kovalev told BoxNation after the win.
"I am confident of more to come. Many people around the world believed in me, maybe not in Britain but I did it."
A bad night for the hometown crowd began in the chief support bout when Gary Buckland lost his British super-featherweight title to Stephen Smith courtesy of a fantastic uppercut finish.
Smith, having taken three of the first four rounds, caught Buckland coming in with the counter-punch in round five.
The one positive result for the locals was Enzo Maccarinelli's redemption, claiming the Commonwealth light-heavyweight title back from Ovill McKenzie.
Maccarinelli was controversially stopped by the referee in their first bout last September, but responded by entering the return fight in much better shape and having the better of the bout for 11 rounds, save for a testing middle portion.
Like Smith, the veteran finished the titlist with a huge uppercut finish for the win in the penultimate round.