And they responded with Chris Wood deservedly putting them ahead with a right-footed finish from the left of the penalty area.
That arrived at the end of a sweeping move involving Heaton, Ashley Westwood, Dwight McNeil and Ashley Barnes, as Dyche’s team repeatedly carved through the visitors.
They pressed home their advantage before the interval, when 19-year-old McNeil turned in Westwood’s cross at the far post.
It was a disappointing end to a strong December for West Ham, who arrived in east Lancashire on the back of five wins from six games.
Despite the return of Marko Arnautovic, playing for the first time since injuring his hamstring at Cardiff on 4 December, Manuel Pellegrini’s side were sluggish throughout with their best chance, a header from substitute Andy Carroll, drawing a fine save from Heaton late on.
The only crumb of comfort for the Hammers was that both Wood and Barnes spurned several excellent opportunities after the break to make Burnley’s win more emphatic.
The win lifts Burnley above Fulham into 18th and level on points with 17th-placed Southampton, who lost to Manchester City.
A run of six defeats from their last seven games has raised question marks over the Dyche’s position for the first time in his six-year tenure.
While the club finished seventh in the Premier League last season, that success was largely constructed upon a solid defensive base.
In stark contrast, the Clarets defence has been porous this term – leaking 41 goals so far, two more than the entire 2017-18 campaign.
And with failed attempts to combat that problem including the deployment of five defenders in their last three matches – all ending in defeats – Dyche reverted to type with a 4-4-2 formation.
Wood and Barnes offered physicality in a two-man attack and club captain Heaton’s return to the line-up proved inspired.
Over 15 months had elapsed since Heaton dislocated his shoulder at Crystal Palace – the last time he featured in a league game for Burnley – but the 32-year-old exerted his influence on those in front of him, barking out instructions and providing organisation and leadership.
That contributed to West Ham managing just four shots on target and Heaton’s understanding with his team-mates was evident as he raced out of his goal in the 15th minute to instigate the move that ended with Wood’s goal.
Heaton positioned himself to calmly head the ball to Westwood under pressure from West Ham attackers, and he underscored a good day’s work by superbly tipping Carroll’s header on to the woodwork late on.
