Grant Hanley scored his first Rovers goal to secure three priceless points and a famous victory away to Premier League champions Manchester United.
Yakubu had fired Rovers into a two-goal lead - scoring from the spot on 16 minutes after Chris Samba had been tugged back in the box and then firing through the legs of David De Gea six minutes into the second half.
But just 23 seconds later, Dimitar Berbatov reduced the deficit with a close-range header and the Bulgarian, who netted five at Old Trafford against Rovers last season, grabbed his second of the afternoon from Antonio Valencia's cross.
With the game hanging in the balance, it was Rovers who scored the all-important fifth, Hanley heading home a Morten Gamst Pedersen corner on 80 minutes to move Rovers off the foot of the table.
Before the game, Rovers made two changes to the side that held Liverpool to a 1-1 draw on Boxing Day.
Both changes came in midfield, with Ruben Rochina replacing the injured Junior Hoilett, who was ruled out with a hamstring strain, and Radosav Petrovic coming in for David Dunn, whose wife gave birth to a baby daughter yesterday.
The home side started brightly, with Nani seeing plenty of the ball early on, but a couple of long-range efforts failed to trouble Mark Bunn, who continued to deputise for the injured Paul Robinson.
Against the run of play, Rovers opened the scoring just past the quarter-hour mark. Following a foul by Patrice Evra on Mauro Formica, Bunn took the free-kick to Samba, who was hauled to the ground by Berbatov inside the box.
Yakubu stepped up and coolly sent goalkeeper De Gea the wrong way.
Yakubu scores from the spot
United continued to dominate possession and carved out a number of half-chances.
On 28 minutes, Nani's corner from the left was flicked on by Berbatov to Phil Jones, but the former Rovers defender's goal-bound shot was blocked by his own player, Javier Hernandez, and the visitors managed to scramble the ball clear.
A minute later, Evra played the ball into the feet of Hernandez, who turned quickly and fired a snap-shot just past the post.
On 32 minutes, neat interplay from United ended with Nani lashing the ball over the bar.
United piled on the pressure just before the break, but Rovers stood strong. Evra picked out Nani, who stabbed the ball goalwards, but Bunn was equal to the save. From the resulting corner, the ball dropped to Hernandez, who was denied by the legs of Bunn at his near post.
Nani registered the first effort of the second half, cutting inside Formica, he again blazed over the bar.
A minute later and Rovers were in dreamland. Adam Henley took a throw-in to Yakubu, who rode the challenge of Michael Carrick, skipped past Jones and fired through the legs of De Gea. It was the Nigerian's 12th Premier League goal in just 13 starts.
Yakubu fires home Rovers' second goal
But straight from the restart, United pulled one back. Valencia's cross from the right wasn't dealt with by Steven Nzonzi and Rafael's shot was headed home by Berbatov from close range.
Six minutes later and the scores were level. Again Rovers failed to clear their lines, Valencia got round the outside of Henley and his centre was turned in by that man Berbatov.
Rovers regrouped and then enjoyed one of their best passages of possession. And on 71 minutes, Formica's shot deflected just wide off Carrick and from the resulting corner, Hanley beat De Gea to the ball, but his glancing header went wide.
In almost carbon copy circumstances, Rovers regained the lead 10 minutes from time. A superb run and shot from Henley earned a corner and from Pedersen's delivery, Hanley got up above De Gea and headed home at the second attempt.
Grant Hanley scores Rovers' winner
Berbatov threatened to score his second hat-trick in six days, but the Bulgarian headed over on 85 minutes.
United laid siege to the Rovers goal in the closing stages, but Jones was again denied by a team-mate in time added on, as substitute Will Keane blocked his shot on the line.
Rovers end the year on a high, with four points from trips to Anfield and Old Trafford for Steve Kean's side, who move up to 18th in the table.
Next up is Stoke City at Ewood Park on Monday January 2nd (kick-off 3pm).
MANCHESTER UNITED: De Gea, Rafael (W. Keane 85), Carrick, Jones, Evra (c), Nani, Valencia, Park, Welbeck, Berbatov, Hernandez (Anderson 46).
Subs not used: Lindegaard (GK), Fryers, Cole, Pogba, Diouf.
ROVERS: Bunn, Lowe, Samba (c), Hanley, Henley, Rochina (Morris 55), Nzonzi, Petrovic, Pedersen, Formica (Goodwillie 85), Yakubu (Slew 90).
Subs not used: Kean (GK), Linganzi, Vukcevic, Blackman.
Booked: Nani, Carrick (Manchester United) Lowe, Petrovic (Rovers)