QPR took the lead at Loftus Road through Barton's low drive just before the break after Swansea had failed to clear their lines.
The hosts doubled their advantage when Mackie turned superbly before firing a low deflected drive beyond Michel Vorm - despite replays showing Mackie to be marginally offside.
Buzsaky capped a fine display with a rasping third, driving an unstoppable shot into the top corner beyond Vorm's despairing dive.
QPR boss Mark Hughes admitted before the visit of Swansea that if QPR are to stand a chance of survival they must win all of their home games - and this was not a bad way to start.
The remaining two are against Tottenham and Stoke and, given the teams that have left Loftus Road without a win this season - Arsenal, Liverpool and Chelsea to name but a few - QPR may yet pull off a great escape.
They were on top for much of the first half but, like Swansea, struggled to create many chances of note, with Mackie coming closest when he was denied from close range after being picked out by Nedum Onuoha from the right.
Swansea created one real chance in the first 45 minutes - a blocked effort by Scott Sinclair from Danny Graham's knock-down.
Just as a forgettable first half was limping towards a stalemate, Barton pounced.
Seizing upon Angel Rangel's headed clearance from Adel Taarabt's wicked delivery from the right, Barton took a touch and rifled inside the near post from 16 yards.
Rather than let the lead slip, QPR maintained their high-intensity game into the early moments of the second half and Swansea, despite possessing some nice touches in midfield, struggled to deal with the sheer might of QPR's midfield.
So it was no surprise when QPR grabbed the crucial second courtesy of Mackie. Latching onto Anton Ferdinand's ball forward Mackie was marginally offside. But it was not spotted and Mackie's deft turn took him clear of Williams, he shifted the ball past Steven Caulker and drilled in his shot in off Rangel's leg.
Once the second went in, Swansea's heads dropped and QPR were rampant.
Buzsaky was impressive throughout and was rewarded with one of the best goals to be scored at Loftus Road this season. Cutting in from the left after Swansea had left themselves exposed, the Hungarian let fly with a beautiful strike that swerved away from Vorm and crashed into the net.
Swansea were valiant and never abandoned their passing game but are perhaps running out of steam at the end of a successful campaign.
But for QPR, it was a welcome win after three successive defeats and keeps them two points clear of trouble.