Riise struck once in each half with Florent Sinama Pongolle, Steven Gerrard and Luis Garcia also on target in what turned into an easy one-sided romp for the Merseysiders, who won for only the second time on the road in the Premiership this season.
How Liverpool must wish they could play Albion in every match as in the four Premiership meetings between the sides, they have scored 16 goals and conceded none.
They could even afford the luxury of seeing Milan Baros miss a 38th minute penalty - conceded by a hand ball from Cosmin Contra that earned the Romanian international a red card.
Even before the loss of Contra, Albion were struggling to keep Liverpool in check.
They had gone into the game hoping that history would repeat itself having beaten Liverpool 1-0 at Christmas 33 years ago when they were also five points adrift at the bottom of the table.
But that never looked likely and they have now taken just one point from Bryan Robson's seven games in charge and are in real danger of being cut adrift.
Robson has massive problems to contend with as his side have conceded a nightmare 16 goals in the last five games and failed to score for the previous three.
The impressive Gerrard went close with two early long-range drives, before Liverpool survived their only major scare of the game.
A misplaced header from Jamie Carragher in the 14th minute fell invitingly for Albion striker Geoff Horsfield. He homed in on goal only to be denied by a last-ditch challenge from Sami Hyypia.
It was a rare scare and was a let-off that Liverpool cashed in on just three minutes later.
Albion's defence was split in two by a sublime through ball from Gerrard. Riise ghosted in behind Contra and was presented with the simple chance of beating goalkeeper Russell Hoult from six yards.
It was an advantage that Liverpool should have gone on to double seven minutes before half-time only for Baros to miss from the spot.
Referee Rob Styles had no option but to point to the spot when Contra handled the ball while keeping out a header from Antonio Nunez following a right-wing corner from Gerrard.
After Contra was dismissed following his impromptu impression of a goalkeeper, Baros strode forward to take the penalty, but it was a weak effort from Baros and Hoult was able to dive low to his left to beat away the spot-kick.
Even when the loose ball found its way back to Baros he was no more successful with his second attempt that was cleared off the line by Darren Purse.
Fortunately for Baros, Albion never looked capable of cashing in on his miss.
The result was put beyond doubt after 51 minutes when Pongolle picked out Riise and raced into the area to steer home a left-wing cross from the Norwegian and score his first league goal of the season.
Liverpool were in cruise mood after Pongolle's strike and Gerrard capped another outstanding display with his seventh goal of the season.
After Purse fouled Baros on the edge of the area, Dietmar Hamann rolled the free-kick to Gerrard who saw his low strike zip past Hoult.
Riise then set the seal on his own starring role by cutting in from the left wing eight minutes from time to fire a thunderous drive past Hoult after Albion had failed to clear a cross from Nunez.
But he was still not finished and Riise turned creator again two minutes from time to set-up Luis Garcia for a simple tap-in from almost on the goal-line.