Stones scored his first Everton goal on Sunday in the impressive 3-0 win over Manchester United.
From the way Stones shrugged off Antonio Valencia and expertly glanced Baines' corner past David de Gea, he looked like a seasoned professional of 15 years.
But this is just the 20-year-old's second full season at the club
The centre-back was plucked from hometown club Barnsley two-and-a-half years ago by David Moyes.
The Scot would have been forgiven for cheering with joy as his final signing for Everton played a big role in the hammering of the club that sacked him after just 10 months in charge.
Not only did Stones score Everton's second, he also kept United's stellar cast of attacking talent at bay, and Baines was keen to praise the imposing centre-back after the final whistle.
"His composure for a lad of his age is unbelievable," the Everton left-back told Press Association Sport.
"He is a down-to-earth kid that he just wants to play football, work hard, he doesn't get involved in anything else and when you are around people like that you just want to see them be successful - and that is the road that John is on at the moment."
After being named on the standby list for the World Cup, Stones started his first England match in September against Norway.
The centre-half began a crucial qualifier in Switzerland the following week but he has not played for the senior team since.
Injury kept him out of the matches against San Marino and Estonia in October and the player has since dropped down to the Under-21 squad.
Once the European Under-21 Championship is over, Stones is sure to be promoted to the seniors again - provided he continues to put in the kind of display he did on his 24th outing for Everton this season.
"He is going to continue to grow and develop as a player and he is going to be a top player for Everton and England," said Baines, who has 30 England caps.
"He has got a huge future ahead of him at international level because not only is he a top-class defender but because of his composure as well
You need a bit of that at international level.
"You need to be able to play and when you look at the young centre-halves around the country, John is the best in that respect."
Source : PA
Source: PA