Kai Havertz headed in the only goal but was also lucky to avoid a second-half red card that could have swung the title race back in Manchester City’s favour.
The Gunners could be crowned champions as early as Tuesday should City fail to win at Bournemouth.
Even if City do end the Cherries’ 16-game unbeaten run and beat Aston Villa, Arsenal will secure the title with victory at Crystal Palace on Sunday.
“One more to go,” said Arsenal boss Mikel Arteta.
“We have done our job, what is in our hands. We have to wait and see what is going to happen tomorrow and then it’s time to prepare for the Palace game.”
However, the narrow margin of victory against a Burnley side that have long since been relegated does offer City hope.
An Arsenal draw at Selhurst Park would allow City to snatch the title on goal difference if Pep Guardiola’s team win their final two matches.
To add extra intrigue to the final days of the season, reports on Monday suggest Guardiola will leave City after a decorated decade in charge after Villa visit the Etihad on Sunday.
Roared on by an expectant capacity crowd in their final home game of the season, Arsenal were tipped to put the Clarets to the sword with ease.
Burnley have taken just two points from their last 10 matches but made Arteta’s men work for the three points on another nervy night at the Emirates.
Leandro Trossard struck the post from the edge of the area before Bukayo Saka saw a penalty appeal waived away as he attempted to turn in Havertz’s low cross.
Arsenal were forced to rely on their set piece threat once more to prise Burnley open.
Havertz rose highest to power in Saka’s delivery on 37 minutes as they scored from a corner for the 18th time in the league this season.
Yet the floodgates did not open and Arsenal were very fortunate not to have to defend their lead with 10 men for the final quarter.
Havertz raked his studs down the calf of Lesley Ugochukwu in a mistimed challenge.
Despite a VAR review, the original decision of a yellow card was not upgraded to red.
Havertz was quickly replaced by Viktor Gyokeres. The Swede’s arrival failed to kickstart Arsenal as an attacking force.
But their rock solid defensive record again edged them closer to the title.
Since losing to City last month, Arsenal have not conceded in their last four league games.
“The margin should have been bigger but we haven’t achieved that,” added Arteta.
“We have shown what we have shown all season that when we need to defend and get through the game, we can do it in an efficient way.” (AFP)
