Drogba outmuscled Steve Finnan and fired in at the near post before Lampard headed in an injury-time fifth.
After securing Alonso's services, the Champions League finalists will now turn their attentions to Steve Finnan and Mohamed Sissoko.
Keane dismissed reports that he had been tracking former Liverpool right-back Steve Finnan, claiming he was happy with his options in that position.
Riera's joins Liverpool following the earlier news on transfer deadline day that Steve Finnan was moving in the opposite direction for an undisclosed fee.
Their first chance came when Steve Finnan played David Edwards onside but, one-on-one, Liverpool keeper Charles Itandje made an impressive stop from the Luton forward.
The energetic Talbot was at the heart of their pressure but, finding himself in an inviting shooting position on 37 minutes after Steve Finnan's error, he screwed the ball lamely wide.
Former Tottenham midfielder Kevin-Prince Boateng pulled one back with a fierce shot from Steve Finnan's cross in the 59th minute, then Defoe saw red for a stamp on Aaron Mokoena two minutes later.
Portsmouth sold Glen Johnson and Peter Crouch over the summer, with nine other players also leaving, but to date their only notable signings have been Brown, veteran full-back Steve Finnan and Watford striker Tommy Smith.
When I watched the game against Manchester City recently, when the Anfield crowd voiced their anger at Liverpool's attitude, Jamie Carragher and Steve Finnan got the ball two or three times on the halfway line.
BBC: SPORT | Football | My Club | Liverpool | Houllier faces mounting pressure
After a low-key opening Wales took the lead in the 23rd minute, with Koumas sending a well-directed header beyond Irish keeper Shay Given after Joe Ledley had beaten Steve Finnan to deliver an inviting cross from the left flank.
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