Rovers' recent record at St. James' Park came to an end thanks to Demba Ba.
The Senegal international scored a hat-trick to condemn Rovers to their first defeat in six visits to Newcastle.
Rovers started poorly and Newcastle took full advantage, Demba Ba opening the scoring on 27 minutes, turning well in the box to fire home.
Three minutes later and the striker was in the scoresheet again, this time nodding home Steven Taylor's headed cross.
Junior Hoilett offered Rovers hope of a come back when he netted just before the break, but Ba soon added his third after the restart, beating Givet to head home to complete his hat-trick.
To compound a miserable day, Rovers had to play the last twenty minutes with ten men after Martin Olsson was sent off for a second bookable offence, whilst Scott Dann also limped off through injury.
Manager Steve Kean made just the one change from the side that defeated Arsenal last time out in the league.
Into the side came Martin Olsson, replacing Ruben Rochina who dropped to the bench. Michel Salgado shook off a knock that forced an early exit from the win over the Gunners to take his place on the right side of defence, meaning Jason Lowe would move back to his usual central midfield place.
Despite being on a high from consecutive victories, Rovers were slow out of the blocks at St. James' Park. The home side seeing early pressure with a series of corner kicks, Demba Ba firing over when well placed whilst Leon Best shot over Paul Robinson's bar from just inside the area.
The match was played a slower than usual pace, but as Newcastle stepped it up, they took a 27th minute lead.
It was lax from Rovers as Mauro Formica allowed fellow Argentine Fabricio Coloccini to bring the ball out of defence, he found Leon Best on the right and he took advantage of Chris Samba being equally slow to close him down. The former Coventry man having time to cross for Demba Ba who turned with his back to goal to fire into the corner of the net for his first Newcastle goal.
Three minutes later and Ba was celebrating his second. After a corner was cleared Danny Simpson's centre saw Steven Taylor out jump Michel Salgado at the back post, Jason Lowe unwittingly helped it on to Ba who needed no second invitation to nod home.
It looked worrying for Rovers, two goals down with barely a sniff of a chance.
But with eight minutes before the break Rovers pulled a goal back with pretty much their first attack of the game.
Mauro Formica intercepted a wayward pass from Ryan Taylor before advancing forward, he switched play to Martin Olsson on the left and his cross picked out Junior Hoilett in the area who took a touch before lashing the ball high into the net past Tim Krul.
Moments later Hoilett escaped the clutches of three Newcastle players as he danced into the area but he couldn't pick out Olsson at the back post as Danny Simpson cleared for a corner.
But it was from that corner that Newcastle would have the last chance of the half. As Hoilett's centre was cleared, Gabriel Obertan raced upfield but the Frenchman shot narrowly over to Rovers' relief.
Rovers certainly started the second half better than they had done in the first, Martin Olsson at the fulcrum of everything that was good.
The Swede very nearly teed up Junior Hoilett for his second of the game, but as he stood the ball up to the back post Coloccini got in a vital header to thwart.
Seconds later and a cross from Michel Salgado found Olsson but his looping effort beat Krul but bounced off the top of the crossbar.
That would be as good as it would get for Rovers as their afternoon quickly turned into a nightmare.
On 54 minutes Demba Ba claimed his hat-trick goal, a Cheik Tiote ball to the back post found the Senegal international, and he rose high to head beyond Paul Robinson and into the corner of the net. Rovers players were incensed as Scott Dann appeared to have been fouled by Leon Best as he did his best to clear the ball on the line. Martin Olsson was booked for his protests.
To make matters worse, the Rovers defender would soon limp off, unable to continue after the challenge from the Newcastle man.
That saw Rovers make one change that was enforced, Ruben Rochina on for Dann, whilst Jason Roberts was brought on for Mauro Formica.
But despite the changes it was the home side forcing the pace, Ryan Taylor had Robinson scrambling with a free-kick, whilst Obertan lashed wide from the edge of the box.
Then on 70 minutes to compound matters Rovers were reduced to ten men. Martin Olsson receiving his marching orders after picking up a second yellow card for what was a tame tug on Leon Best.
Only great defending from now makeshift left back Jason Lowe prevented Newcastle from getting a fourth on 74 minutes. MIdfielder Yohan Cabaye skipping his way into the area before beating Robinson but Lowe was there to get across and clear.
A man down Rovers were struggling to contain the home side, Leon Best turning Chris Samba but firing over, and in a bid to add more steel, Yakubu was sacrificed for Vince Grella.
That helped stem the tide towards the Rovers goal, but aside from a Steven Nzonzi drive that flew over, they could little to stop Newcastle claiming their first league win over Rovers since 2004/05.
NEWCASTLE: Krul, Coloccini (c), Cabaye, Simpson, R. Taylor, Gutierrez (sub Marveaux 84 mins), Ba (sub Ben Arfa 74 mins), Best, Tiote, Obertan, S. Taylor.
Subs not used: Harper (GK), Guthrie, Lovenkrands, Perch, Ameobi.
ROVERS: Robinson, Salgado, Samba (c), Dann (sub Rochina 63 mins), Givet, Hoilett, Lowe, Nzonzi, Olsson, Formica (sub Roberts 64 mins), Yakubu (sub Grella 79 mins).
Subs not used: Bunn (GK), Petrovic, Vukcevic, Hanley.
Booked: Lowe, Nzonzi, Olsson (Rovers).
Off: Olsson (Rovers).