Teenager McCarthy drilled home the opener a minute before half-time, after the hosts had lost first-choice goalkeeper Tomas Cerny to injury following a collision with Chris Porter.
McCarthy doubled his side's lead shortly after the hour mark with an eight-yard strike, securing the three points which allowed Accies to draw level with their arch-rivals at the bottom of the table.
Although Hamilton remain in 12th place, the promoted side are now separated only on goal difference from today's opponents.
The Motherwell side showed two changes from the team which had lost at home to Kilmarnock five days earlier.
Paul Quinn returned from suspension and Jamie Murphy was promoted from the bench in place of midfielders Bob Malcolm, one of the substitutes, and Stephen Hughes, who dropped out of the squad.
Accies captain Alex Neil returned from a knee ligament injury.
Richard Offiong carved the first chance after three minutes when his headed flick to McCarthy on the right was played back into his path by the teenager.
Offiong bore down into an exposed Motherwell penalty area but visiting goalkeeper Graeme Smith smothered his effort.
Home goalkeeper Cerny was poleaxed in an early collision with Porter, but continued after treatment.
Stevie Hammell tried an ambitious long-range effort from the edge of the box, but his diagonal drilled strike rolled harmlessly wide.
Murphy had a chance for Motherwell just after the half reached its midway stage, heading narrowly wide of the right-hand post from a Hammell ball.
At the other end, James McArthur set up Offiong for an effort which was scrambled clear, and he then had a header caught under the bar.
Motherwell's response was a 35-yard effort from Quinn which Cerny beat down at the left-hand post.
Porter went even closer 11 minutes from the interval with a sudden turn and shot just inside the area which the Hamilton goalkeeper stretched to claw out from under the top-left corner.
It proved to be Cerny's last action, as he then had to be substituted for Sean Murdoch.
However, the game burst into life a minute before the break when Hamilton took the lead.
The ball was headed on to McCarthy on the right and the teenager coolly sprinted towards goal and fired a diagonal effort which beat Smith to nestle in the bottom left corner.
It was followed by controversy as Motherwell centre-half Maros Klimpl appeared to stamp at Brian Easton following a challenge on the halfway line, but he escaped with only a booking.
Mensing had a snapshot just minutes into the second half, but his shot whipped in from an acute angle on the right whistled past.
Porter tried to create an opening for a Motherwell equaliser, but his cross from the right flashed along the face of goal and evaded strike partner John Sutton.
Hamilton suffered another injury blow seven minutes after the restart when defender Mark McLaughlin had to be stretchered off after being clattered heavily by his own keeper when Murdoch leapt out to punch the ball clear.
The treatment delay and three substitutions which shortly followed caused a lull in the game with attacks at a premium as the sides continued their physical battle.
Motherwell substitute Jim O'Brien tried an ambitious curling ball from the left but it did not unduly trouble Murdoch.
However, Hamilton then doubled their lead as the second half reached its midway point.
The visiting defence completely failed to deal with a long ball launched towards the penalty area, and McCarthy needed no second invitation to latch onto it and roll home his second of the game from eight yards.
Motherwell staged a mini-rally as the game entered its final stages with some headed efforts, one of which Porter saw clutched by Murdoch.
Youngster Saunders then barrelled out of his own half and scampered all the way down the right flank, but his eventual shot was well off target.
The visitors' best effort came eight minutes from time when Mark Reynolds had an effort saved from a Hammell corner and then Darren Smith's rebound was cleared off the line at the right-hand post.
Hamilton continued to press in the five minutes of injury-time, and Mensing came close with a late close-range effort after being played in by Joel Thomas.