Australia were wobbling after Tomljanovic's torrid Fed Cup debut against Mladenovic, but a beaming Barty strode onto court cradling her niece in her arms and soaking up a huge ovation from the packed crowd.
Barty's clinical victory in just 56 minutes made it 1-1 in the best-of-five format, ahead of Sunday's reverse singles and potentially a doubles decider at RAC Arena. "I started my year off here and it's a hell of a way to finish it off".
But in searing 38 degrees Celsius heat she kept her cool to embarrass a stunned Caroline Garcia in a rare double bagel, with the Frenchwoman having no answers to the Barty armoury in front of 13 000 fans. "I was really in the zone".
The French Open champion, wrapping up a breakthrough season, was imperious, firing down pinpoint first serves and effortlessly pushing Garcia around the court, forcing errors.
Ashleigh grabbed the first game of the second set with another ace, breaking in game two with a forehand victor and racing into a 3-0 lead after a service victor.
Barty wrapped up the first set in 29 minutes and there was no let up as she sent down 11 forehand and four backhand winners.
Team captain Alicia Molik will weigh up whether to substitute Tomljanovic from the singles - most likely for the vastly experienced Stosur - after she had been overcome by nerves while representing Australia for the first time against a red-hot Mladenovic.
Barty will now face Mladenovic first on Sunday before Tomljanovic takes on Garcia.
"I couldn't have asked for a more flawless match", Barty said.
"I think that's probably the best tennis match I've ever played in my life", an elated Barty said. "I love these sort of matches, the bigger the pressure, the more special the event".
Mladenovic also struggled to find the first serve but no one noticed that after facing only one break point and delivering six successful return games to control the scoreboard all the time. Tomljanovic lost serve in the very first game after netting a backhand, falling 3-0 behind after a forehand victor from Mladenovic who hit a double fault in the fourth game to keep Ajla in the set. But it did not last long with the French number one's powerful forehand proving too hot to handle.
Tomljanovic's serve further disintegrated in the second set as Mladenovic roared to a 5-1 lead before sealing the match when Tomljanovic slapped a return well beyond the baseline.