Sean Dyche did well to keep a lid on his emotions in the wake of Arsenal’s hugely controversial winner three minutes into stoppage time of a contest which only came to life after the interval.
Wenger simply accepted his 20th anniversary present from referee Craig Pawson with a modest gratitude, a gift-wrapped error from the officials which of course he failed to lay his eyes on, again.
“I didn’t see it go in,” the 66-year-old claimed in trademark style of the dramatic last-ditch intervention that broke Burnley hearts.
Alex Oxlade-Chamberlain and Laurent Koscielny slashed at a Theo Walcott’s flick from an Alexis Sanchez short corner and the ball eventually went in off Koscielny's hand to make it five straight wins for the Gunners, who climbed to third, two points behind leaders Manchester City.
Wenger had other things on his mind in the lead-up to the decisive goal.
“I was fuming because we played the short corner at the end of the two minutes. I was asking why didn’t we take the direct corner?
“I didn’t see it go in, but I’ve been told that we were fortunate to get the goal. It’s a big win because City lost today.
“We were five points behind them and when you get a chance to get closer you can’t miss it.”
Koscielny couldn’t claim not to have seen it like his manager, and after literally grabbing his second goal of the campaign, the 31-year-old centre-back insisted: “You have to respect the referee’s decision.”
Defeat was hard on Burnley, who pushed the Gunners all the way. “It’s frustrating,” said Dyche.
“They score six seconds over the two minutes of added time. It doesn’t sound a lot, but the referee could have blown it at the short corner.
“There’s a number of things. It’s a handball goal so you’re frustrated when you’ve not even got a kick left in the game afterwards.
“I’ve not been to see the referee, but I can only think he is honest enough and will have a tough night driving home.”
For long spells, Wenger’s troops looked like they had misread the party memo because they appeared to have been out celebrating the Frenchman’s anniversary weekend in the lead-up this disjointed display.
Far from leaving battling Burnley punch-drunk, the Gunners looked to be suffering from the mother of all hangovers as Wenger’s landmark game threatened to go downhill in the rolling Lancashire Moors.
Burnley remain 14th on the back of another hard-working performance full of character, as they continue to impress on their return to the top flight following promotion in May.
They came closest to breaking the deadlock with 15 minutes left, recalled keeper Petr Cech touching defender Michael Keane’s header against the bar as Arsenal posted a fourth consecutive clean sheet, a run spanning more than six hours.
Cech had also been forced to save well from a Johann Berg Gudmundsson header early in the second-half as the Clarets aimed for a repeat of their victory over Liverpool here earlier in the season.
Arsenal rarely looked in danger at the outset of their latest visit to Lancashire even though the hosts wasted the clearest opening of a forgettable first half short on both entertainment and chances.
Wales international Sam Vokes should have done much better when he headed wide from near the penalty spot after meeting Matt Lowton’s cross.
It was an opening against the general run of play, as Arsenal enjoyed two-thirds of possession and greater territory without making their dominance pay.
They were rationed to half-chances by a Burnley back four in which Chelsea target Keane again excelled.
Sanchez saw his angled drive deflected inches wide by defender Ben Mee in an early foray, before Walcott fired across the face of goal.
It was early in the second half when Tom Heaton was called on to make his first save, the Burnley keeper diving smartly to his left to hold a close-range effort from Sanchez, after some intricate build-up play from Walcott and the otherwise anonymous Mesut Ozil.
Sanchez went even closer to the deadlock-breaking goal inside the final 20 minutes, grazing the post with a close-range volley, as Arsenal’s late pressure eventually told in a heart-breaking finale for Sean Dyche’s side.
The Burnley manager added: “Apart from the last six seconds, I thought the referee had a good game.”
Heaton 7; Lowton 7, Keane 8, Mee 7, Ward 6; Marney 7, Hendrick 6; Gudmundsson 6, Defour 6 (Arfield 62, 6), Boyd 7; Vokes 6.
Bamford, Robinson, Flanagan, Kightly, Tarkowski, O’Neill.
Cech 7, Bellerin 6, Mustafi 7, Koscielny 7, Monreal 6, Cazorla 6, Xhaka 5 (Elneny 71); Walcott 6, Ozil 4, Iwobi 6 (Oxlade-Chamberlain 71); Sanchez 7.
Ospina, Gibbs, Gabriel, Holding, Reine-Adelaide..
Craig Pawson 5