Accrington Stanley were unbeaten and Stevenage without a point going into the match but it took just 6 minutes for the home team to get off the mark.
Brian Quailey was the man with the goal as he coolly headed in Justin Gregory's cross and he set up Ritchie Hanlon for number two.
Goodliffe added the third after good work down the left by Dannie Bulman and the duo comined again to make it 4-0.
Joe Flack notched the fifth from George Boyd's pass but the scoreline flattered Stevenage as Stanley had plenty of chances, Paul Mullin with the best, heading over from close range.
The one positive to come out of the game was the fact that winger Rory Prendergast made his first appearance of the season after overcoming injury, coming on as a sub for Lee McEvilly with 35 minutes to go.