Liverpool dominated the match and Dirk Kuyt opened the scoring after only four minutes when Andreas Isaksson failed to keep out his low drive following a corner.
Keane doubled the lead half an hour later with a flick from Fernando Torres's excellent cross. It was the Irishman's first goal for the Reds since joining from Tottenham and the relief on his face was tangible as he celebrated scoring for the club he supported as a boy.
Steven Gerrard put the result beyond doubt with a sweetly-struck 76th-minute free-kick that left Isaksson no chance. It was Gerrard's 100th goal for Liverpool and sealed a 250th game in charge for boss Rafael Benitez.
Danny Koevermans pulled one back for PSV two minutes later when he got ahead of Martin Skrtel to bundle home a centre from former Reds full-back Jan Kronkamp.
Aside from the goal action, Liverpool had several chances to add to their tally, with a hard-working Torres close on several occasions.
PSV were hampered by the decision of coach Huub Stevens to employ no conventional strikers in a formation that saw Nordin Amrabat as the most advanced player until Koevermans was brought on as a second-half substitute.
The Dutch side's star man, Ibrahim Afellay, missed the match through injury and his influence was also notable in its absence. PSV stay bottom of the group after conceding five goals and scoring only once in two matches.
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