Nonda volleyed Rovers into a ninth-minute lead, before Yakubu levelled the scores from the spot. But McCarthy bagged his 11th of the campaign to inflict a festive defeat over Boro for the second year running.
Boro boss Gareth Southgate made two changes to the side that drew 0-0 with Everton last time out, with James Morrison and Mark Viduka replacing Julio Arca and Gaizka Mendieta.
Boxing Day's goalkeeping hero Brad Friedel recovered from a dead leg, as Rovers boss Mark Hughes named an unchanged side following the thrilling 1-0 victory over Liverpool at Ewood Park four days earlier.
Despite the torrential conditions and buoyed by the victory over Rafa Benitez's side, Rovers came flying out of the traps.
On three minutes, David Bentley dug out a cross from the right, McCarthy nipped in front of his man before cutting the ball back to Morten Gamst Pedersen, and his fierce shot was blocked on its way to goal.
But just six minutes later, Rovers did make the early breakthrough. Andy Todd's defensive clearance found Lucas Neill on the halfway line. The Australian supplied a first-time ball over the top and Nonda arrived on cue to strike a dipping volley past Mark Schwarzer from the edge of the box.
The DR Congo captain, a season-long loan signing from Italian giants AS Roma, made his first start for the club against the Teessiders back in September and crowned the occasion with his first Rovers goal in a 1-0 win.
Rovers continued to press, with Bentley and Brett Emerton both firing wide, before Boro registered their first attempt of the game on 23 minutes, through James Morrison's wayward shot.
Rovers looked in control for much of the first half and almost extended their lead a minute before the break following a fine passing move, but McCarthy's curling shot was comfortable for Schwarzer.
The home side continued where they left off after the break, with two good moves in the opening 10 minutes. Gamst opted to pass to McCarthy when a strike on goal was surely the better option, before Bentley almost found the South African with a pin-point right-wing cross.
But against the run of play, the visitors were handed a lifeline when Neill pulled Emanuel Pogatetz to the ground inside the box just before the hour and Yakubu stepped up to roll the ball into the bottom left-hand corner, sending Friedel the wrong way.
Minutes later, Neill went on a surging run all the way into the Boro box only to be brought down by Pogatetz but, on this occasion, referee Martin Atkinson awarded a goal kick.
But with a quarter-of-an-hour remaining, Rovers grabbed a deserved winning goal. Gamst's corner was punched clear only as far as Robbie Savage. The Welshman delivered the ball back into the danger area and McCarthy rose highest to head the ball into the roof of the net past Schwarzer.
Nonda, McCarthy, Bentley and substitute Matt Derbyshire all had chances late on to make the points safe, but Rovers weren't to be denied a second successive home win.