Like Parker, Leeds boss Daniel Farke has vast experience of getting out of the Championship.
He did so as champions with Norwich City in 2019 and 2021 and has now led the West Yorkshire club back to the Premier League after bouncing back from play-off final heartache against Southampton a year ago.
Farke told BBC Sport: "Of course I'm happy that we won this game in the final stages and are officially allowed to label ourselves as champions and the best team this season.
"It's an emotionally moving day because we have invested so much and wanted to crown ourselves with some silverware.
"It feels pretty, pretty special in the dressing room and I'm very happy for my players and staff, it means so much for them, and also our supporters."
Nobody should forget Sheffield United, either. Although four defeats in five games in April, including a loss at Burnley which ultimately knocked them out of contention for automatic promotion, proved fatal, the Blades led for long periods and looked the most likely.
Chris Wilder's side will need to go again in the play-offs, starting against Bristol City in the semi-finals. They have shown their readiness for the Premier League this season, finishing on 90 points, a tally which would have been enough to go up automatically in three of the previous six seasons.
While that points to a more competitive top of the Championship than ever, successive seasons with all three promoted clubs coming down, including Burnley and the Blades, offers a stark warning too.
A strong defensive unit will be crucial to hopes of survival, and Clarets captain Josh Brownhill, who also scored 18 goals, believes his team have a strong chance of improvement this time around.
"This is a different team, we look in really good shape to go up for next season and hopefully stay up. It is going to be difficult but we've worked hard on everything; our defensive record speaks for itself," he told BBC Radio 5 Live.
"Credit to the staff and the fans but mainly the gaffer. He has worked harder than anybody. 100 points, unbeaten at home, unbeaten in 33 games, our defensive record has been exceptional."
Never before have two teams accrued so many points in the same season at the top of the second tier.
Their consistency and strength of character laid the groundwork. Leeds held their nerve in the end, and right at the end, but ultimately, both they and Burnley can revel in achievements fit for the history books.