An experimental Liverpool side won at Bournemouth to record a third consecutive victory in all competitions.
Roberto Firmino's rebound and Daniel Sturridge's header gave the visitors a commanding 2-0 lead at half-time.
Bournemouth rallied after the break but Joshua King's stoppage-time strike came too late for a comeback.
The result lifts Liverpool up to seventh place in the Premier League table, while the Cherries remain 13th.
Liverpool made 10 changes from Thursday's momentous Europa League win over Borussia Dortmund as manager Jurgen Klopp named an inexperienced side.
The fringe players repaid the German's faith with an accomplished performance which preserved their record of having never lost against Bournemouth.
Liverpool still have a slim hope of finishing in the top four but winning the Europa League is their likeliest route to Champions League qualification - and Klopp's selection suggested he agrees.
Wales goalkeeper Danny Ward made his club debut and young defender Connor Randall was given a first Premier League start.
Jordon Ibe and his fellow winger, the less experienced Sheyi Ojo, shone as the Reds' youngsters seized control of the first half.
However, it was two established first-team players who made the most telling contributions.
Top scorer Firmino opened the scoring from a rebound after Artur Boruc had saved Sturridge's audacious backheel, before the England striker headed in Ibe's free-kick just before half-time.
A European hangover is an ailment which has undermined Liverpool's Premier League campaign.
Their victory against Stoke on 10 April was only the second time in eight attempts that Klopp's side had won after a Europa League fixture this season.
However, this mature display suggests the Reds are capable of finishing the campaign strongly on both fronts.
With six games left in the Premier League, Klopp now faces a balancing act between Liverpool's domestic commitments and a Europa League semi-final against Villarreal.
Given Leicester's extraordinary title challenge, Bournemouth's first Premier League campaign has somewhat passed under the radar.
A run of four wins from their previous six games had Eddie Howe's side targeting a top-half finish, though this defeat is a setback to those hopes.
Bournemouth were competitive throughout against Liverpool, testing Ward on numerous occasions in the second half.
Their perseverance was rewarded with King's low strike in added time, even if the goal was ultimately in vain.
Man of the match - Jordon Ibe
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