England emerged at 116-5 chasing a target of 268 with Wyatt and Kate Cross at the crease, but Gardner's devastating performance put paid to their hosts' slim hopes of victory in a single session.
The off-spinner picked up all five final day wickets to go with the three she had on day four, beginning with getting Cross caught behind on 13 runs to deny England the start to the day they needed.
Amy Jones was next to depart, losing her wicket for four runs, after she charged down the pitch only to see Gardener's delivery beat the outside edge and go through to Alyssa Healy, who completed the stumping despite a fumble.
Sophie Ecclestone was dismissed lbw for 10 runs before Gardner bowled Lauren Filer for a duck and wrapped up the victory by getting Wyatt (54) out lbw to finish with figures of eight for 66 in the innings and 12 for 165 in the match - both Australian women's cricket records.
"I wouldn't have dreamt of it but I guess it just shows that having five days in the test match is incredibly important," said Gardner, who was named player of the match.
"As a bowling unit we just said to keep the stumps in play as long as possible. It was just awesome to put a performance on for the team."
The win give holders Australia four points in their quest to retain the Ashes and the teams now move on to the three match Twenty20 International series that begins on July 1 at Edgbaston.
"I really thought we were going to do it this morning, so I'm pretty disappointed," Wyatt said. "It was pretty hard to bat out there.
"There is a sense of missed opportunity, we will have a chat in the changing room about it. There are a lot of positives so we have to try to dust this down and smash them in the white ball stuff.
"There's a few tired bodies out there and now we just need to dust ourselves off and get ready for the next challenge."
