It was the Lilywhites' first win at The Hawthorns since October 1973 and it was a thoroughly deserved one.
Ryan Lowe's men were the better side throughout, dealing comfortably with Albion's agricultural long ball game - the hosts didn't manage an effort on target.
Riis gave them the lead in the 41st minute, getting the last touch on the line after Greg Cunningham's cross had deflected goalwards off Kyle Bartley.
The three points were wrapped-up 14 minutes from time, Cunningham's shot parried by WBA keeper David Button and Archer followed-up to head home.
A large following of the PNE faithful celebrated wildly when Archer's goal went in and even more at the final whistle as the players and PNE manager Lowe took the applause in front of the away end.
It was a third win under Lowe's stewardship in a decent start for him.
The North End side had seen three changes from last Saturday's defeat at Swansea, with Ryan Ledson, Andrew Hughes and Brad Potts returning.
Ledson filled the midfield vacancy left by Daniel Johnson being away on international duty with Jamaica.
Hughes slotted back on to the left side of the back three, that releasing Cunningham to play at left wing-back, with Potts resuming at right wing-back.
PNE had the game's first chance in the third minute, Ledson playing a corner short to Ben Whiteman who swung a cross into the box.
It was met by Hughes in the middle who sent a header wide of the far post.
Riis had a big shout for a penalty turned down when he was clipped by Cedric Kipre from behind in front of goal but referee Keith Stroud waved play on.
Whiteman's 30th minute free-kick to the far post was met in the air by Cunningham who headed down into the goalmouth, David Button grabbing it on the floor.
Alan Browne's nicely-weighted pass into the box found Riis on the angle, the striker driving a first-time shot over the bar.
North End's first-half defensive duties mainly consisted of cutting out long balls.
It needed a good piece of covering from Ledson in the 37th minute when former Preston loanee Adam Reach cut the ball back from the left-wing into the path of Alex Mowatt on the edge of the box.
Ledson got in a challenge just as Mowatt connected, his shot travelling over the bar.
PNE went in front four minutes before the interval with a well-worked goal.
Ched Evans got the ball on the left hand side of the box and knocked it back to Whiteman, the midfielder threading a first-time pass behind the home defence to free Cunningham.
The Irishman drove it across goal, the ball striking Kyle Bartley and travelling towards the net - Riis stretching out his right foot to get the last touch on the line.
Sepp van den Berg put in two great tackles within a few seconds of one another at the start of the second half as Albion got into the PNE box in search of an equaliser.
A great opening fell North End's way to stretch their lead in the 52nd minute, Evans chasing a ball forward to get behind the home team's back line.
He took the ball wide of keeper Button down the left wide of the box, checked back and squared it into the middle to find Riis but the Dane sliced his volley and the chance went begging.
Ex-PNE striker Callum Robinson, on as a substitute, put a shot wide from the edge of the box.
Archer came on for his Preston debut in the 64th minute, replacing Riis, and within 12 minutes had opened his PNE account.
Browne led a counter-attack down the left-wing, driving through the Albion half before slipping a pass to the overlapping Cunningham down the side of the box.,
Cunningham drove in a shot which Button parried up into the air, Archer following in to head into the roof of the net from close range despite the efforts of Bartley on the line.
WBA: Button, Furlong, Kipre (Gardner-Hickman 46), Bartley, Townsend, Reach, Mowatt, Livermore (Molumby 72), Diangana, Grant, Phillips (Robinson 56). Subs (not used): Palmer, Clarke, Faal, Fellows
PNE: Iversen, Van den Berg, Bauer, Hughes, Whiteman, Potts, Browne, Ledson (McCann 83), Cunningham, Riis (Archer 64), Evans (Maguire 74). Subs (not used): Ripley, Lindsay, Sinclair, Rafferty.
Referee: Keith Stroud (Hampshire)
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