It was the home side's first Super League defeat of the season and the visitors' maiden league win of this term as the title race was opened up.
Linlithgow had no answer to a Whitburn side, who controlled the game for 80 minutes before allow
ing Rose a glimpse of a draw in the final stages.
Linlithgow boss Fairley said: "That was our worst performance of the season and not one player in the dressing-room can hold his head up and say he did all right.
"In the end, it would have been unfair to Whitburn if we had grabbed an equaliser in the last ten minutes."
Whitburn attacked the Linlithgow defence from the kick-off and scored a dramatic opener after only two minutes.
Colin Strickland flicked a ball out wide to Chris Dolan who made ground before sending over a low teasing cross to the back post. The Linlithgow defence were caught napping as Alex Lurinsky came running in at the back post to bundle the ball over the line.
Linlithgow were being overrun by a Whitburn midfield who never gave them time on the ball, battling for every ball.
They scored a second in the 25th minute. A Chris Dolan corner from the right again caught out a hesitant Linlithgow defence and as the ball fell to Andy Doig he laid it back to Kevin Donnelly who was in a better position. His 25-yard drive flew past the keeper and almost burst the net for a super finish.
Whitburn continued to dominate but to keep them on their toes Linlithgow's Gordon Herd produced a terrific turn and shot in the 37th minute which smacked off the bar and over.
The second half saw Whitburn on the defensive as Linlithgow started strongly. However, they didn't threaten and once again Whitburn started to dominate.
The first real chance of the half fell to Linlithgow's Mark Robertson but keeper Stewart Walker was up for it with a good save.
Whitburn were looking comfortable and Strickland almost scored their third but keeper Steven Pinkowki brought off a good stop.
The introduction of Gary Livingstone to the right wing for Linlithgow allowed Sean Grady to go through the middle. It almost paid immediate dividends when Grady controlled a loose ball but once again Walker saved well.
Linlithgow looked down and out but were given a lifeline after Whitburn played a sloppy pass in the centre of midfield. Stuart McArthur picked up the ball and ran at the defence. He cut inside and from 20 yards he blasted the ball. It took a slight deflection on its way into the net to reduce the deficit.
Linlithgow then had their best spell of the game but just to remind them that the game wasn't over Whitburns central defender Colin Leiper ran with the ball for 40 yards before shooting wide.
Whitburn then ran out the game to remind Linlithgow that there is a huge Citylink Scottish Junior Cup game coming up between the side in two weeks time and they had the upper hand this time.
Linlithgow manager Fairley didn't mince his words to his players. He said: "They were told in no uncertain terms that this type of performance is not acceptable.
"The last ten minutes were too little too late. We should have been playing like that from the kick-off. Credit to Whitburn for the way they played their game."
Whitburn boss Derek Strickland was delighted with the result, saying: "It was good to see that we dominated the game from the kick off.
"We had a great start after only two minutes and that showed us we could win this game. We were strong where it mattered, and scored goals when it mattered.
"At half time I told the players that Linlithgow would come at us but we were holding them comfortably until we gave them a chance.
"The homework we did before the game paid off. I said before the game that once we got our full squad back we would improve and that's what happened.
"We now have two games in hand and that keeps us in contention.
"There's still a long way to go in this league because it's not won in October, but Saturday was a good win for us and will give the players a lot of confidence going into the next few weeks."
Linlithgow; Rose: Pinkowski, Robertson, Waugh (James), Gallagher, King, Bradley, Grady, Tyrrell, McSween (Livingstone), Herd (Geddes), McArthur.
Subs: Wilson, Hogg.
Whitburn: Walker, S Murphy, Leiper, Mooney, McGurk, Donnelly (J Murphy), Hannah (D Murphy), Doig (McNelis) Lurinsky, Strickland, Dolan.
Subs: MacKay.
