Everton will feel unfortunate not to have grabbed a victory, and even though Arsenal needed more than a draw to keep the pressure on the Premier League pace-setters, ultimately boss Arsene Wenger will have been grateful to share the spoils.
The Toffees were able to recall Marouane Fellaini after suspension, while influential midfield man Mikel Arteta recovered from the rib injury that kept him out of Sunday's FA Cup tie against Liverpool at Anfield.
Arsenal made six changes from the side that drew at Cardiff in the FA Cup - but there was little opportunity for anyone to shine in a dour first 45 minutes.
Wenger pleased with Arsenal spirit
Everton showed plenty of endeavour, but their lack of attacking options was exposed as they failed to mount any sort of sustained threat on Manuel Almunia's goal.
Cahill headed wide from Arteta's corner, while Van Persie could not control his close-range effort from Samir Nasri's cross.
Matters livened up after the break, with Denilson wasting Arsenal's best chance when he was off target from Van Persie's pass and Cahill shooting into the side-netting with an angled drive.
Cahill's ability to find space in the box is uncanny, and Arsenal became the latest victims when he put Everton ahead after 61 minutes.
We deserved a victory - Moyes
Baines delivered an inviting cross to the far post, and Cahill rose superbly to head firmly beyond Almunia.
Arsenal's failure to show any of their trademark passing game had been their biggest failing, especially when faced with the sort of defensive discipline that has become Everton's trademark in recent months.
Cahill, the game's outstanding performer, almost added a second after 82 minutes with a stinging drive that bounced away off Almunia's chest.
Van Persie had been Arsenal's best hope of fashioning an equaliser, but he was receiving little positive support from his Arsenal team-mates.
Everton were concerned late on when Cahill limped off after an innocuous challenge, and boss David Moyes will be hoping it is not a recurrence of the metatarsal problems that have dogged his recent career.
It did not look likely to deny Everton victory, but Van Persie showed his quality with seconds remaining, taking Abu Diaby's pass on his chest before lashing a left-foot volley beyond Tim Howard.
Everton manager David Moyes:
"We feel bad because the players were terrific. We deserved the victory and to have it taken away right at the end is very disappointing.
"Tim Cahill is doing a magic job for us. He has got a goalscoring record like a centre-forward. He is scoring like a striker should. I wouldn't say he is making it look easy but he is doing great.
"He went off injured but I don't think it is too bad. He took a kick on the foot but hopefully it is not too bad."
Arsenal manager Arsene Wenger:
"When you are 1-0 down with a minute to go and you get a point you are relieved. It was a game where two teams gave everything and we showed quality and character.
"We showed fighting spirit, passion and intensity and Robin van Persie scored an exceptional goal.
"We can pass the ball better but you have to give a lot of credit to Everton. They play in an intelligent way and play a kind of game that made a passing game very difficult.
"It is a game we wanted to win but it was one we couldn't afford to lose so maybe it is not too bad."
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