The Reds broke the deadlock in the first half when England striker Sturridge beat United goalkeeper David De Gea from the penalty spot after Nathaniel Clyne was brought down by Memphis Depay.
Liverpool duo Adam Lallana and Philippe Coutinho spurned chances to double the home side’s lead before half-time as Klopp’s side dominated their bitter rivals.
However, Roberto Firmino handed the Reds a commanding 2-0 first-leg lead with 17 minutes remaining after good work from Jordan Henderson and Lallana down the right wing.
Klopp is gradually transforming Liverpool into an energetic, coherent unit, in a way that Van Gaal has failed to do with Manchester United.
— Gary Lineker (@GaryLineker) March 10, 2016
Liverpool’s 2-0 win was their first victory over their bitter rivals United in four attempts.
Van Gaal’s host West Ham United in the FA Cup quarter-final at Old Trafford on Sunday afternoon before Liverpool travel to Manchester for the return leg.
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