After a dire first half Stockport finally succumbed to the home side's superiority to cave in as they looked destined for relegation this season.
Swindon saw most of the ball throughout the game and had the better of the chances in the first half.
After good work by Sam Igoe in the 29th minute the ball fell kindly to Smith who saw his toe-poked shot smothered by keeper James Spencer.
On-loan striker Jamie Slabber, who was making his first start for Swindon, showed some neat touches throughout the first half and had two long-range efforts which forced keeper Spencer into saves.
After the interval Swindon continued to press and finally made their dominance pay off just after the hour.
Smith's corner from the right was only half-cleared and Heywood curled in a delightful left-foot shot from the edge of the area for his first goal of the season.
Just seconds later, another Smith corner reaped reward when captain O'Hanlon was on hand to head in number two from just six yards.
With Stockport reeling, Swindon capped off an amazing 180 second period, when Smith turned from provider to scorer with a superb left-foot shot from 30 yards.
Slabber, on loan from Tottenham until the end of the season, almost scored his first in Swindon colours after good work by Igoe.
The midfielder's centre allowed Slabber to break free into the box only for Spencer to come quickly off his line to deny the young striker a shot on goal.
Stockport were poor throughout and showed why they're propping up the League One table - they failed to gain a single corner, and didn't have a shot on target until the 82nd minute.