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The record nine-times League Cup winners beat Fulham 3-2 on aggregate and will meet Chelsea in the Wembley final on Feb 25 in a repeat of the 2022 final that Liverpool won on penalties.
Diaz scored in the 11th minute when he chested down a high ball in the box before cutting inside and launching a shot that took a deflection before sneaking in the near corner.
Issa Diop injected some life into the Fulham fans when he equalised in the 76th minute, kneeing home a pinpoint pass from former Liverpool player Harry Wilson.
Fulham kept pressing until the final whistle in some nerve-wrangling minutes for Premier League leaders Liverpool.
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