Rogers scored 101 runs from 233 balls while somehow surviving the bowling of Stuart Broad, who took four Australian wickets for 48 runs at Chester-le-Street.
The men in Baggy Green reached stumps on 222 for five, before bad light stopped play prematurely, to trail England by just 16 runs.
The 35-year-old Rogers said: “[It feels] pretty bloody good to be honest. I’ve had a long career and didn’t think I’d get this opportunity, let alone to score a hundred. To get a hundred is the best moment of my career.
“To play for your country is unbelievable. To wear the Baggy Green and get a hundred is something no-one can take away from you. I’m extremely happy at the moment. I think when the ball is harder it’s seaming and it’s swinging so that’s the challenge so you just have to ride your luck, and I had plenty of luck today.
“On these wickets you can’t push out at the ball or you’ll nick it or miss it so the key is just to hold your shape as long as possible.”
Rogers rejected suggestions that Australia are starting to dominate after building momentum at Old Trafford, only for rain to force a draw and allow England to retain the urn.
“I don’t know about that, I think there’s a long way to go,” he added. “We need to get a lead and this wicket’s not going to get any better.
“If we can get through and things keep going our way then hopefully we can get on the board.”
It was a particularly good day for Nottinghamshire’s Broad who, despite being thwarted in his attempts to dislodge Rogers, took the wickets of David Warner, Usman Khawaja, Michael Clarke and Shane Watson – the first three falling inside the first 14 overs.
“It was a really good day but credit obviously has to go to Rogers,” Broad said. “He was gritty and he played the line so if it seamed he played and missed most of the time.
“He took his runs when they were available and it was a well put together hundred.
“He’s put his team in a decent position but from an English point of view, with the new ball round the corner tomorrow, if we get early wickets then we’ll be in a strong position.”