In hindsight, they would have been better off just completing the single and hugging, after Mitchell was bowled the next ball for 101 by one that stayed low from Curran.
It marked the first time since Mark and Steve Waugh's centuries against England at The Oval in 2001 that Australian brothers have reached three-figures in the same innings.
Close off the field, the brothers provided the perfect balance for each other in their maiden century stand of 169.
"We don't have too much banter," Mitchell told ABC on Sunday.
"Shaun is pretty serious out on the field and I'm not. I just try and keep him as relaxed as possible."
Earlier the celebration for Shaun's century was far more controlled.
After he went to stumps at 98 not out on Saturday night, the 34-year-old drove England offspinner Moeen Ali to the cover boundary off the fifth ball of the fourth day to bring up his second ton of the series.
The Marsh brothers immediately raised their arms aloft as the ball beat the infield, before their first emotional embrace mid-pitch.
Shaun's sixth career Test century capped off a remarkable summer for the West Australian, who has become the Aussies' most consistent batsman aside of Steve Smith.
Left off Cricket Australia's contract list last year, the older Marsh was dropped for the August tour of Bangladesh before being a controversial recall for the Ashes in what would be his ninth Test life.
However, he has rewarded selectors with a stunning series that has included fighting 50s in Brisbane and Melbourne to go along with his centuries at the WACA and SCG.
While Shaun was patient and waited for the loose balls, Mitchell was explosive for the most part of his second century of the series after being recalled for the third Test.
He scored just three of his first 30 deliveries, before bringing up his hundred off his 140th ball as Australia rammed home a lead of more than 200 in response to England's 346.
-AAP
