The Yorkshiremen combined for a 191-run partnership in Colombo to lift England to a mammoth 3-357, the highest total on this ground since 2018.
Root steered the innings with an unbeaten 111, laying the platform for skipper Brook to issue a stunning reminder of his firepower as he blasted Sri Lanka to all parts of the ground in an ODI-best 136 not out from just 66 balls.
On a ground where scores above 300 are rare, it was a total always likely to be beyond the hosts and so it proved despite a wonderful maiden international century from Pavan Rathnayake.
For England it was just a second ODI series win in their last eight and provided a morale boost after the 4-1 Ashes drubbing as well as aiding their ODI ranking, with automatic qualification for the 2027 World Cup far from certain.
An impressive 2-1 win, against a side who had won seven consecutive 50-over series on home soil, will also come as a relief to under-fire head coach Brendon McCullum.
Brook began this tour admitting he was lucky to still be captain after an altercation with a nightclub bouncer in New Zealand on their last white-ball engagement.
In the circumstances his celebration, mimicking WWE fighter "Stone Cold" Steve Austin's "beer smash", raised eyebrows.
"It was just more about celebrating tonight with the boys," Brook explained. "Like I said the other day in my press conference, I've got to try and gain that trust back with the lads and the way I wanted to do that was perform, play well and lead from the front."
Root said there was "no malice" behind the gesture and he "hoped it would be received the right way".
"He's trying to show he wants that approval from the group, through humour," said Root.
"That's another area of why he's going to be a great leader, because he has that side to him as well.
"He's showed his calmness and his clarity under pressure, and he's also showed humour as well in doing that."
Brook went from 50 to 136 in 26 balls after Root backed up scores of 61 and 75 in the first two matches with a 20th ODI century.
Jacob Bethell played his part with a well-made 65.
Sri Lanka began their daunting chase on the charge and were 2-94 off nine overs but then Pahum Nissanka went for 50 off 25 balls and they fell away.
Rathnayake's 121 kept Sri Lankan hopes alive but he was the last to fall as they were bowled out with 3.2 overs to spare.
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