Joey Gudmundsson's long-range effort was heading well wide until it deflected off Ashley Barnes to completely wrong-foot Chelsea 'keeper Thibaut Courtois.
It took Chelsea five minutes to restore its lead with Moses left unmarked to fire in Emerson's cross from the left.
Fellow Spain global Cesc Fabregas attempted to calm the striker down, as Chelsea held on for a 2-1 win and kept their slight hopes of a Champions League place alive.
The wingback's goal was just the second of the season in 24 league appearances.
Conte said: "We played a good game against a hard team because it is not simple to play against Burnley".
They were accomplished going forward despite the absence of Cesc Fabregas and Willian, while Eden Hazard appeared only as a second-half substitute. But that's also down to the Blues winning way less these days.
"I'm really pleased with our growing mentality", Dyche told Sky Sports.
Chelsea fielded two centre-forwards - Alvaro Morata and Olivier Giroud - in tandem for the first time in seven years and the duo linked well.
"We believe in the players we've got collectively and individually. But we are talking about a good manager", Conte said.
"I think Alvaro must be angry because when you have a chance to score, you have to score, especially for a striker", said the Italian.
While this was acceptable last season, Chelsea didn't have Champions League football to contend with back then, meaning that the team were virtually getting a week to recuperate after each game.
The two matches took place today instead of Saturday.
Chelsea will to be looking to salvage a trophy from a despertely disappointing season when they face Southampton for a place in the FA Cup final. As it turned out, Conte was thoroughly vindicated by an excellent team performance. "They put great pressure on the ball in every moment".
While obviously simply frustrated by another fruitless run-out (he has one league goal since December), Morata still felt the need to come out and explain/apologise for his most minor of hissy fits after the match...
"Maybe with this desire, with this will to fight, this will to get a result, we have the possibility [to reach the top four]".