Kyah Simon scored a brace to ensure Australia needs only a draw with Sweden in their final group match on Wednesday morning (AEST) to advance to the knockout stages.
Simon, one of three changes to the line-up that lost 3-1 in a spirited showing to the United States, took the glory with a goal in each half.
But the Matildas had plenty of contributors against a disjointed Nigerian side who struggled to create chances.
Chief among them were captain Lisa De Vanna and Laura Alleway, with Stajcic revealing the pair played through the pain barrier against the African champion.
"Laura Alleway was on crutches for two days and Lisa was on crutches for three up until yesterday," he said.
"We were fairly bruised and battered after the American game ... for them to come out and play 90 minutes is just fantastic."
De Vanna was crucial in the Matildas' opening goal, bustling past two defenders and releasing Simon just as she was hacked down by a third.
Simon finished well on her non-preferred left boot past Nigerian goalkeeper Precious Dede.
In the second half, Sam Kerr turned provider, flicking a ball over the African defence which Simon lashed home with her right.
Stajcic praised the Matildas for building on their first-up loss to the US.
"It was a tough game, a tough battle in the heat," he said.
"Today, we were more clinical and it's what we weren't the other day."
The Matildas emerged from the Nigeria contest with a clean bill of health, with the possible exception of Kerr.
The tenacious forward was viciously elbowed in the face behind play late in the match in a clash that went unnoticed by the referee.
After treatment, Kerr returned to the field to play out the match, with Stajcic saying she had a sore jaw that was possibly broken.
"Sam doesn't go down easy - she looked in a fair bit of discomfort," he said.
"If it requires x-rays tonight, we'll have to send her to the hospital.
"Hopefully, it's not (a broken jaw) - we suspect she's ok."
The Matildas move from Winnipeg, the host of their first two matches, to Edmonton for the clash with Sweden.
"They've probably got four or five of the best players in attack at this World Cup," Stajcic said.
"Everything's up for grabs still. We have to put a good performance against Sweden and seal our spot in the next round."
The US, among the tournament favourites, was held to a goalless draw by Sweden also in Group D.
The Americans, who started with captain Abby Wambach on the bench, were given a tough test by the Swedes, who played out a 3-3 draw with Nigeria in their opener.
The US leads the group with four points followed by Australia with three, Sweden on two and Nigeria bottom with one.
In the final round of group games on Wednesday morning (AEST), the US-Nigeria and Sweden-Australia showdowns will determine which nations go through to the last 16, but a draw for the Matildas will be enough for them to advance.
