Dover suffered their first loss in pre-season after the League 2 visitors scored in each half.
Jamie Reid put Stevenage ahead before Chris Lines doubled their lead in the second half.
Reid struck inside the first 10 minutes after he got on the end of a high through ball from Jake Reeves to fire past Josh Bexon, giving the keeper no chance.
Shortly after, Whites were almost level through Gillingham loanee Henry Woods, who forced the visitors trialist goalkeeper into a great save after great work from TJ Bramble to keep the ball under huge pressure from the Stevenage defence.
Ricky Miller then went close after Aaron Cosgrave won a free kick on the edge of the area, however, his shot deflected off the wall and out for a corner.
From the resulting corner, Ryan Hanson went close from Sam Wood’s cross, glancing his header over the bar.
Whites started the second half strongly and were almost level through Ben Williamson, who got on the end of a deep cross from Miller and it needed a good save to deny him.
From the resulting corner, Whites went close again, this time Jake Goodman heading wide from Wood’s corner.
Goalkeeper Adam Parkes, who replaced Bexon at half-time, produced a couple of stunning saves to deny Stevenage, but there was nothing he could do to keep out Lines’ stunning free-kick.
A trialist almost got one back for Whites in the closing minutes after getting on the end of a great cross but he was denied spectacularly by the visitors keeper.