Without Mesut Ozil, ruled out with illness, the Gunners lacked the guile and trickery to break down a superbly-marshalled Burnley defence.
And the prospect of losing both the German playmaker and the match-winning Chilean striker cannot fill any Arsenal supporters with enthusiasm.
Indeed, the one takeaway from this hard-fought victory is, surely, that Arsenal can forget about any sort of title bid this season if both are allowed leave in January.
Sanchez was presented with the chance to win the game when James Tarkowski pushed Aaron Ramsey in the back in the 92nd minute. Moments earlier, Arsenal had failed in a similar appeal, after Robbie Brady tackled Hector Bellerin in the area, and Wenger felt there was no doubting the validity of the decision.
“From outside it looked 100% a penalty,” said Wenger. “I don’t know why he pushed him with two hands in the back. There was one on Bellerin as well. I can understand why they were disappointed but, from our side, it looked a penalty.”
Burnley manager Sean Dyche agreed that referee Lee Mason had made the right decision at the death although questioned whether a small club such as his own would have been given the award.
“There was no problem with Ramsey at all,” said Dyche. “That was a smash in the back compared to what most people go down with in this division, there was a definite nudge in the back. So probably it gets given but we’ve had a lot not given like that. I don’t know why”
Sanchez’s penalty conversion was impressive and a victory was just about merited as the Chilean made a major impact in a much-improved second-half display from the visitors.
“I pushed him more in the middle in the second half and he was much more influential,” said Wenger.
“I felt in the first half he was like the team. He didn’t get into it enough but the second half was much better, more dangerous. You could see through him danger could be created.”
Traffic delays meant Arsenal only arrived at Turf Moor 50 minutes before kick-off, having just lost Ozil to illness.
“The doctor came to see me and said Mesut had to travel back,” said Wenger. “He was in the hotel with us, but then travelled back. Will he be available for Wednesday? We’ll see what it is.”
Slow out of the blocks, it took a fine save from Petr Cech to deny Johann Berg Gudmundsson.
Cech also kept out a Brady free-kick as Arsenal were limited to operating on the counter-attack — an Alexandre Lacazette cross which Ramsey shot high over the bar being their best opening.
But after the restart Arsenal began to assert control and only supreme defending from Tarkowski and Ben Mee kept them at bay.
Substitute Jack Wilshere might have won the game with a shot deflected behind off Tarkowski.
But in the end, this game went the way of last season’s two meetings between the clubs, although at least Sanchez’s winner here came as “early” as the 92nd minute, as opposed to his 98th-minute winning spot kick against Burnley last season.
Pope 7; Lowton 6, Tarkowski 8, Mee 9, Ward 6; Gudmundsson 7, Defour 6 (Wood 78, 6), Cork 7, Brady 7; Hendrick 6; Barnes 6. Subs (not used) Lindegaard, Vokes, Westwood, Bardsley, Long, Arfield.
Cech 6; Koscielny 7, Mustafi 7, Monreal 7; Bellaerin 6, Ramsey 7, Xhaka 6, Kolasinac 7; Iwobi 6 (Wilshere 66, 6), Sanchez 8; Lacazette 6 (Welbeck 78, 6). Subs (not used) Ospina, Mertesacker, Giroud, Maitland-Niles, Coquelin.
L Mason (Gt Manchester) 5