The striker claimed his eighth hat-trick for the club after just 40 minutes at Kenilworth Road, before the hosts struck back with two goals from Jordan Clark.
Haaland then bagged two more before Kovacic blasted in a stunning strike to secure progression into the quarter-finals of the competition.
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Haaland made more history as he became the first player ever for the club to score five times on two separate occasions after netting a quintuple in the Champions League last season against RB Leipzig.
“Incredible. Incredible. Five goals in a game is unbelievable,” said Kovacic after the game.
“His mentality is to score goals and to be there fighting. Today I think his overall game was amazing. Not just the goals.
“He’s a player that you love and enjoy to have in your team.”
The Croatian also spoke about his first domestic goal for the club, touched on the team’s hunger to retain their FA Cup crown and spoke about this weekend’s upcoming Premier League Manchester Derby.
