Johnson headed home a wonderful cross from Charli Grant in the 38th minute in front of 43,020 fans at Marvel Stadium, and won't care that she appeared clearly offside.
Australia doubled their lead in the 69th minute when Kaitlyn Torpey shanked a cross into the top corner.
Interim boss Sermanni, who has coached the Matildas across three stints, appears likely to finish up after Monday night's second game in Canberra.
Joe Montemurro is widely expected to take on the full-time job after the current international window.
The Matildas' starting line-up had just 438 combined caps heading into the game - with Emily van Egmond and Alanna Kennedy claiming 293 of them.
Captain Steph Catley and Arsenal teammates Caitlin Foord and Kyra Cooney-Cross didn't play after arriving in camp on Wednesday night following their Women's Champions League triumph.
Sam Kerr, Ellie Carpenter, Hayley Raso, Katrina Gorry and Mackenzie Arnold aren't in the current squad.
But Australia still had 16 shots (six on target) to six, while Argentina didn't register a shot on target until the 80th minute.
Johnson, who had scored three goals in six games for Calgary Wild in Canada's Northern Super League, was among Australia's best, impressing with her deft footwork and strength on the ball.
Six minutes into the match, Johnson burst down the left and cut the ball inside for Holly McNamara, who couldn't keep her shot down.
Another six minutes later, McNamara latched onto a cross from Charli Grant but couldn't turn her volley on target.
In the 15th minute, Florencia Bonsegunda cracked a long-range strike over the bar - which would prove Argentina's only shot for the half.
The Matildas struck in the 38th minute when Grant burst down the right flank and curled a superb cross to the back post for Johnson to head home.
Replays showed the attacker was offside but there is no VAR in friendlies.
Johnson turned her defender then whipped a long-range effort just wide in the 49th minute.
McNamara couldn't keep a speculative shot down in the 61st, while she forced Argentina goalkeeper Chaves into a save four minutes later.
Torpey scored when she attempted to launch a cross into the area but didn't hit it cleanly, and watched on in disbelief as it nestled in the goal.
Chaves made a good save to deny Wheeler at the near post in the 72nd minute and the Matildas couldn't find a third goal.
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