Purvis underlined his Olympic ambitions to win gold for the third consecutive year, recording an impressive 91.550 score.
And the podium was completed by two gymnasts who missed the recent European Championships due to injury, Youth Olympic gold medallist Sam Oldham taking silver and former world silver medallist Dan Keatings securing bronze.
British selectors now face some tough decisions when they meet to consider the make-up of their team early next month.
Purvis and Olympic pommel horse bronze medallist Louis Smith should be considered locks for two spots on the five-strong team.
Proven performers Oldham and Keatings's displays are timely while Kristian Thomas, Max Whitlock and Ruslan Panyeyleymonov - fourth, fifth and sixth at the nationals - are also pushing their claims.
"It feels brilliant to win the national title and hopefully it's looking encouraging looking ahead to team selection," said Purvis.
"My form over the year has been good, so it's looking positive, I'm just waiting for the phone call now."
Keatings has suffered a succession of injury problems since winning all-around silver at the 2009 World Championships in London.
But he believes he's done enough.
"The last couple of months have been really tough for me battling through injuries but I tried to stay positive and this was always my focus," he said.
"I knew I had to smash it and prove I'm still right up there with the best.
"I know selection will be a close call but I just hope I've done enough and proved I can compete under pressure."
Oldham also believes his performance should be enough to claim one of the coveted spots on the team.
"It was better than I could ever have hoped for," he said.
"I was the last chance to impress and I really nailed it. It shows that hard work pays off. I've had these trials at the back of my mind for so long and I just tried to remember that I've worked all my life for this moment - and that was a big motivation."
Tunney won the women's national title - a stunning achievement for a 15-year old in her first season as a senior.
Jennifer Pinches claimed silver and defending champion Hannah Whelan settled for third after a fall on the beam.
Three-time world champion Beth Tweddle - competing for the first time after her recent injury - posted top scores on the bars and floor.
"It's just up to the selectors to decide what works best for the Olympics," said Tunney.
"It's my first year so it's totally unexpected. I just wanted to stay clean and maybe get in the top five, so to win is incredible."