Moeen resumed on 26 overnight before being dismissed for 77 by Mitchell Starc as England reached 430 before they were bowled out.
The Worcestershire player then took 2-67 – dismissing Australia vice-captain Steve Smith and skipper Michael Clarke – to help the home side restrict their opponents to 264-5 at the close.
“We are very happy with the start we had with the bat and then to get five wickets, it has been a great effort,” he told Sky Sports.
“A couple of early wickets tomorrow and with the new ball around the corner, I think we are in the driving seat.
“Cooky (Alastair Cook) said for everyone just to play the way they play and I felt (I should) go out and be aggressive and play my shots, try and enjoy it and entertain everyone.”
Moeen struggled at times to cope with bouncers in last summer’s series with India but he looked comfortable against the Aussie pace attack at the SWALEC Stadium and admitted he has been working hard to improve this aspect of his game.
“It’s something I have been working on quite a lot over a period of time now with (England batting coach) Mark Ramprakash,” he added.
“We work on being decisive and clear in what we are going to do and for me, the best way to play is to take it on.
“It’s something I had to work on because I got in trouble against India last year and it was nice to get a couple of pull shots away.”
Australia opener Chris Rogers admitted to some nerves before his 95 in Cardiff.
The 37-year-old, who is playing in his final Test series, somewhat fortuitously clubbed his first Test six but was denied a century as he was caught behind off Mark Wood to leave Australia on 180 for three.
“When I woke up this morning I was pretty nervous so I would probably have taken that 95,” Rogers told Sky Sports. “It’s always disappointing when you get so close and maybe I could have done a slightly better job for the side.”
Asked what was the cause of his nerves, Rogers said: “It’s such a big series, it’s the Ashes, and I don’t really start series well so it was nice to have a good start.”
Rogers announced before the Ashes that this would be his final series, but he insisted he was not feeling any extra pressure.
“I plan to really enjoy this,” he said. “Even though I was nervous, these are opportunities I’ll never get again so I’ve got to make the most of it.”
Rogers admitted that the late loss of Adam Voges, out for 31, perhaps left England on top but he believes the match remains finely balanced.
“I think it was an excellent day of Test cricket, with both teams going at each other pretty hard,” he said.
“England might have the slight upper hand but we’ve got some good batting to come so if we can get a bit closer we’ll put the pressure on and you never know what can happen.
“We’re going to have to play a really good game from here on in.”