Lawes captained his country on his 100th Test appearance (five of which have come for the British & Irish Lions) and he turned in a huge display.
It helped to ensure England bounced back from their disappointing 30-28 first-Test defeat to the 14-man Wallabies on the previous weekend.
And Lawes was delighted with the way his team performed as they took a 19-7 half-time lead before eventually seeing the game out in the second half.
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"It was a tough scrap," Lawes said.
"I'm really proud of the boys.
"We knew they would come back at some point because they've got some quality players and it was tough for a little while, but we came through it.
"We've been working hard to get our strategy right and to get to know each other, and it paid off this week.
"We showed at the end our defence can get us on the front foot but we let them score too easily.
"They scored two pretty simple tries and in international rugby you can't really have that.
"Our fans were unbelievable here and we want to thank them. We're glad we could put on a performance for everyone back home as well."
Lawes was joined in the England starting line-up by Saints team-mate Tommy Freeman, who enjoyed a successful Test debut at Suncorp Stadium.
And Lewis Ludlam also played a part, coming off the bench during the second half to deliver a typically strong showing.