The visitors might have scored twice in the opening minutes, from set-pieces, with new signing David Unsworth each time going close.
But Scunthorpe gradually found their confidence to take charge of the game with Burnley keeper Gabor Kiraly having an unhappy afternoon.
Twice he flapped at high balls into the box and each time he had to be rescued by his defence.
First Unsworth headed away a goal-bound effort from Ian Baraclough and then Clarke Carlisle also had to head over another goal-bound header from Iron skipper Andy Crosby.
Just before the interval substitute Andy Butler almost gave the home side the lead with a header that looped just over.
It was Scunthorpe who took control at the start of the second half, going in front after 47 minutes when a quickly taken free-kick by Goodwin was flicked by Paul Hayes into the path of Paterson, who drilled a left-foot shot past Kiraly.
Seventeen minutes later Scunthorpe struck again when Jonathan Forte sent Goodwin racing through the middle to beat Kiraly with a right-foot shot from the edge of the box.
Winger Kevan Hurst went close to making it 3-0 with a stinging 20-yard drive that flashed just wide.
Burnley, opening day winners against West Brom, pressed in the closing stages with Unsworth going close to a consolation goal with a header from a Robbie Blake corner that was well blocked away by goalkeeper Joe Murphy.
The result gives Scunthorpe four points from the first six in their bid to prove the bookies wrong and survive at this level.