Lewis O'Brien's strike for the visitors soon after Chaplin's goal failed to spark a comeback.
The result means that Barnsley have now suffered just one defeat in their last eight games while Huddersfield have yet to win in 2020, going down to three straights since the turn of the year.
Following a quiet start, Barnsley struck in the 14th minute when Jacob Brown's low cross from the right-hand side of the area was tapped in by the unmarked Mowatt from close range.
Clarke Oduor then put a free-kick off target for the hosts.
Marcel Ritzmaier, who was making his Barnsley debut after signing from Austrian club Wolfsberger, then fired in a firm drive which was deflected wide.
Huddersfield manager Danny Cowley made a double substitution before the start of the second period, sending on Steve Mounie and Florent Hadergjonaj in place of Karlan Grant and Jaden Brown, and the visitors enjoyed more possession in the early stages of the second half but failed to create an opening.
Barnsley increased their lead in the 65th minute with Brown again the provider from the right-hand side of the area, squaring to Chaplin who fired into the net.
O'Brien pulled a goal back for Huddersfield a minute later with a thumping drive from the edge of the area.
Mounie went close to equalising soon after with a shot on the turn which was touched wide by Sami Radlinger.
Campbell wasted a great chance for Huddersfield, shooting over from a good position after meeting Juninho Bacuna's free-kick. Mounie also fired wide with an effort from just inside the area.
Ritzmaier threatened to break free in the closing stages, losing his footing as he advanced towards the area.
Hadergjonaj and Campbell were both booked in stoppage time as they tried to usher Chaplin off the pitch when he was being substituted.
Keeper Kamil Grabara raced out of his area to clear as Brown looked to burst through.
O'Brien had a shot blocked following a corner deep into stoppage time.