The Clarets have up to four games in hand on some of their relegation rivals and gave their hopes of survival a huge boost despite the remaining bottom of the table.
Nick Pope kept the Gunners at bay despite enjoying over 75 per cent possession and having 20 shots on goal.
Arsenal edge up to sixth but are two points behind fourth-placed Manchester United.
Tottenham also have the chance to move into the top four when they travel to Chelsea later on Sunday.
Leicester's hopes of European football next season were dealt a huge blow by conceding twice deep into stoppage time to lose to Spurs in midweek.
Brendan Rodgers' men were again guilty of giving up a lead as Brighton secured a third consecutive 1-1 draw.
Patson Daka fired home on the rebound after Robert Sanchez had saved from Harvey Barnes in the first minute of the second half.
But Brighton levelled eight minutes from time when Danny Welbeck headed home Neal Maupay's cross.