Things have been far more difficult for Empoli, who lost their first five consecutive matches, leaving them 19th in the league table and at risk of being sucked into a relegation battle.
Liverpool, however, were uncharacteristically tame for a fixture against their fierce rivals and the win lifts United into second place in the Premier League table behind Manchester City.
The result lifts Burnley off the bottom of the table and up to 18th, two points above Sheffield United who drop two places to 19th and remain without an away win this term.
Until then, Everton's organisation and resilience had frustrated the defending champions, who had not managed a shot on target until Haaland struck with 19 minutes to go.