England led 6-0 after 10 minutes and 9-5 at half-time but the Wallabies were the superior outfit throughout the second period.
Adam Ashley Cooper's well-taken try proved the decisive moment of the match, with fly-half Matt Giteau adding the conversion and two penalties after lively scrum-half Will Genia had claimed the visitors' only points of the opening 40 minutes.
Wilkinson, a Test Lion against the Wallabies in 2001 and again in New Zealand four years later, returned from an 18-month absence from the international scene with two penalties and a drop goal in an assured display.
Wilkinson's individual performance provided plenty of positives for England team manager Martin Johnson but the former Lions skipper admitted that there was no doubt the better side had come out on top.
"In the second half Australia dominated to such an extent they're going to score points - eventually penalties or tries are going to get you," said Johnson.
"We kicked away too much ball, which gave it back to them a little bit too easily.
"Overall they deserved to win but there were chances for us to do a bit more. We started very well but lost a bit of control near half-time.
"The team's only playing its first game and at times we needed to be a little bit slicker, but we'll be better for it physically and mentally next week."
Meanwhile in Cardiff a few hours later, Wales were beaten 19-12 by New Zealand.
Wales had been looking for their first victory over the All Blacks in 56 years but a second-half score from hooker Andrew Hore and 14 points from the boot of inspirational fly-half Dan Cater extended that lengthy wait for at least another year.
Lions fly-half Stephen Jones kept Wales in the game with four successful penalties but it wasn't enough to topple Graham Henry's men in front of a sold-out Millennium Stadium.
Lions forwards coach Warren Gatland had picked 13 Lions in his starting XV, with Stephen Jones, Shane Williams and Ryan Jones all having faced the All Blacks with Britain and Ireland's elite in 2005.
And Wales did have their chances against a New Zealand side coming into the game on the back of a 32-19 win over Australia the week end before.
The two teams entered the break level at 6-6 but, just as they had done in the same fixture 12 months earlier, the All Blacks pulled away in the second half to start their European tour with a win.
"It's about learning to play at the highest level, making sure for 80 minutes that we switch on and nail critical moments," said Gatland.
"There are fine things as a team we hammer in at training but we must carry them into the game and keep developing."