The Italian has tasted little but unqualified success since arriving at Stamford Bridge, a well-earned point lifting his side 10 points clear of second placed Tottenham at Turf Moor yesterday.
But the fact that healthy advantage was not an even healthier dozen was down to Brady, who followed his memorable goal for Ireland against Conte’s Italy in last year’s Euros by scoring a superb equalising free-kick after 24 minutes here.
Nemanja Matic tripped Joey Barton on the edge of the area and Burnley’s home debutant, a club record €15 million signing from Norwich in the January transfer window, curled a magnificent 20-yard free-kick over the wall and into the top corner of Thibaut Courtois’ goal.
“It was a sublime free-kick against a top-class goalkeeper, a giant of a man,” said Burnley manager Sean Dyche, as Brady became the first opponent to score a direct free-kick against Chelsea in four years.
“To find that area of the goal was fantastic. To get put into that game was not easy for him. He’s just signed for a new club, he’s getting a feel for how the team works, but he held his own in a really tough game.”
Brady admitted this was not an easy introduction to life at Turf Moor and that, his goal aside, it was not a performance he was particularly pleased with
“I was lucky enough that it went in because I did not have the best of games,” he said.
“I’m glad it managed to get us a point in the end. They don’t all go in like that but luckily today it did. I thought the lads were excellent today.
"It shows what the team are about. The home form is unbelievable and we stuck it out and it is a great point in the end.”
The goal was reward for Burnley’s impressive response to an equally impressive opening from Chelsea that would have swept away lesser opposition after the first goal, a move started and finished by Pedro after seven minutes.
The winger passed to Eden Hazard who, in turn, fed Victor Moses on the right.
After skipping past Brady’s crude challenge, Moses crossed for Pedro, who had covered nearly 70 yards, and his 12-yard shot gave Tom Heaton no chance in the Burnley goal.
Chelsea threatened to simply sweep their hosts away but after weathering that pressure, the hosts began to show why they have become so feared on their own turf.
Dyche’s team should even have taken a lead into the interval after Barton found full-back Matt Lowton who only had Courtois to beat but was denied by a solid block from the Chelsea keeper.
The furious tempo of the game continued after the restart with a mistake by Matic leading to a Burnley attack - Andre Gray capitalised on another error by David Luiz, received a pass from Barnes and shot straight at Courtois.
As the half wore on, however, both teams seemed relatively happy with the status quo, denying Burnley a sixth successive home top-flight league victory for the first time in 56 years but also keeping them well away from any hint of trouble at the foot of the table.
For Chelsea, another game is ticked off the fixture list and a point collected at a freezing, snowy stadium where lesser teams have been found wanting in terms of their character and technical ability.
“I saw great commitment from the team but for sure we must be a bit disappointed to take only one point,” said Conte.
“We put a lot of energy onto the pitch and we took only one point. We must be a bit disappointed for this. We want to try and play and win every game. Today we tried to play football and create a situation.
"We found a team who don’t do this, this long ball and fight for the second ball. But I have great respect for every type of football. I don’t like to judge the others.
“There are 13 games before the end. If someone thinks this league is finished, I can tell you now, no. There are six teams for me that can win the league, anything can happen.”
Heaton 6; Lowton 6, Keane 6, Mee 5, Ward 6; Boyd 5, Barton 8, Westwood 6, Brady 7 (Arfield 64, 6); Barnes 6, Gray 7 (Vokes 82, 6).
Robinson, Darikwa, Flanagan, Tarkowski, Gudmundsson.
Courtois 6; Azpilicueta 6, Luiz 6, Cahill 6; Moses 7 (Willian 72, 6), Kante 8, Matic 5 (Fabregas 67, 6), Alonso 6; Pedro 7 (Batshuayi 87), Costa 6, Hazard 6.
Begovic, Zouma, Ake, Chalobah.
Kevin Friend 7