Gabriel was charged by the ICC on Tuesday after he was warned by the on-field umpires in the third Test in St Lucia for comments made towards Root.
The West Indies should also have sent the third member of England's top three back cheaply but Joe Denly was badly dropped on 12, fending Shannon Gabriel to third slip off the shoulder of the bat only for Shimron Hetmyer to bungle the chance.
But Stokes and Buttler came together for an unbroken fifth-wicket stand of 124 as two of England's traditionally aggressive batsmen, perhaps in light of recent criticism of the side's approach, reined in their natural game to guide their team to a strong position.
"Sometimes things are said on the field but they should stay on the field".
The Sky Sports cricket expert and columnist insisted that while there was now no evidence of any wrong-doing by Gabriel, Root's reaction sent an important message.
Footage from Sky Sports has since emerged of Root responding to Gabriel on the pitch. "Even in the fight of test cricket @root66 shows his class and morals and just what a sound bloke he is!"
Mindful of a forecast of showers later in the day, Root gave both Stokes and Wood spells with the relatively new ball in the quest for more success before the lunch interval.
While another added: "Well said Joe Root, no room for that attitude in sport".
Pybus was unaware of any potential controversy at the close of play but told BBC's Test Match Special: "Nothing has been reported to me but if a comment was made we'll review it and if it was untoward we'll be addressing it".
"It feels fantastic. All the hard times I've had with injury, and the self-doubt, today I feel like an England", said Wood. "It's always a proper tussle out there".
"Shannon is a proper old-school fast bowler, I think we need to find out if there is anything behind the rumors and then we'll address it".
Root enjoyed a fine day at the crease, scoring a 16th Test century and finishing 111 not out as England built a lead of 448 runs.