Liverpool dominated the match, with recently-retired defender Jamie Carragher and a portly-looking Fowler coming on as substitutes.
The goals were easy on the eye, Allen rolling home after fine play by Iago Aspas and Raheem Sterling, while sub Henderson finished well after another good team move.
There was also a sight of wantaway striker Luis Suarez, who was given a rousing reception as he came off the bench in the second half.
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But the show was stolen by Fowler who, at 38, now carries the weight of a man 10 years his senior, but still showed some good touches and almost scored a trademark sliding finish but for a desperate block from a defender.
The Greek side, against whom Gerrard netted a famous goal in 2004, travelled to Anfield to face Brendan Rodgers’ side with Liverpool rolling out club legends Carragher and Fowler for appearances.
Liverpool started positively and created the first real chance in front of goal when Allen flashed an effort across the box, before Aspas had a shot smothered by Megveri in the Olympiacos goal.
Allen was presented with another glorious opportunity, latching on to Aspas’ wonderful back-heel flick over the opposition defence. However the Welsh midfielder fired his effort well over the bar from a matter of yards.
Yet it was Allen who opened the scoring moments later, finishing from close range after Aspas dragged his shot across the face of goal.
The Spanish forward continued to impress and should have found the net himself but his volley on the turn was saved by the legs of the Olympiacos keeper, somehow staying out of the net.
Glen Johnson came close to doubling the home side’s advantage, powering a left-footed drive past the post after cutting inside off the right wing.
Gerrard was pulling the strings from the centre of midfield and almost set up Allen for a second, whipping an exceptional cross into the box where the midfielder was waiting. However Allen mistimed his header and glanced wide of the target.
Sterling - who was heavily involved in the opener - looked lively as the second half got under way and came mightily close to making it 2-0, lobbing a shot inches past the post after being sent through one on one with the substitute keeper, Roberto.
However, Liverpool did double their lead moments after, when Henderson found the net just 12 seconds after being introduced from the bench, latching on to Sterling’s through and clipping over the keeper.
Rodgers sent on Luis Suarez to a positive reception from the Anfield crowd, instantly involving himself in Liverpool’s attacking play and linking up well with new signing Luis Alberto and Philippe Coutinho.
Jose Enrique saw an effort saved well by Roberto after surging forward down the left wing before Fowler, introduced with just over 15 minutes to play, was played through on goal by Gerrard. But the former striker’s effort was deflected over by the Olympiacos defender, lacking the pace to get a clean connection on the ball.
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