The weather held out for the whole game, but is was very cold, with a bit of light snow, and sleet during the game, but it didn't settle on the pitch.
Swindon had more chances to score in the first half with Sam Parkin coming close again with a Steve Jenkins cross, and Roberts also came close to hitting the back of the net.
Hull eqalised towards to end of the first half with a deflected goal from Jonathan Walters going in of Matt Heywood from 12 yards out.
In the second half it was Hull who looked the better side, and most Swindon fans would have settled for a 1-1 draw at this stage.
On 74 minutes Swindon scored their second when Sean O'Hanlon poked in a close range shot following a goal mouth scamble to make it 2-1 to Swindon.
Sammy Igoe should also have scored for Swindon in a one-on-one with the 'keeper but he hit the ball too late which allowed the Hull 'keeper to make the save.
Then on 87 minutes Sam Parkin looked to have the finished the game for Swindon, when with a Swindon player lying injured on the pitch the referee waved play on, so Roberts from able to pass the ball to Parkin to score from 12 yards out.
After setting up Sam Parkin twice during the game Christian Roberts got himself on the score sheet in the final minute of normal time with a close range shot from a Parkin cross to make in 4-1 to Swindon.
In stoppage time Hull scored again to make it 4-2 with a goal from Stewart Elliott after some poor last minute defending.
Swindon pushed forward to try and get a 5th goal, but ran out of time as the referee blew up to end the game.
Overall a very good win for Swindon which moves them up to 7th in the table ahead of next weekend's away trip to Chesterfield. Swindon could have scored 6 or 7 goals, but will settle for the 4. Swindon have now scored 14 goals in their last 4 home games.