The former Argentina Under-20 captain, thrust back into a midfield position to solve the Black Cats illness and injury problems, struck in the 53rd minute to break the hearts of the near 10,000 travelling fans from Teesside.
Marcus Stewart contested a long punt from goalkeeper Mart Poom with Pool defenders Michael Nelson and Chris Westwood, with the ball breaking loose for Arca to beat Jim Provett with a fierce low angled 20-yard drive.
But the home side should have booked their passage into the fourth round much earlier with both Stewart and Arca hitting the post in the first-half while John Oster was just off target with a delicate chip shot with Provett stranded.
Pool had their moments too, Paul Robinson twice going close and strike partner Eifiion Williams forcing Poom into two brilliant one-handed saves.
The Second Division side started the second half in more attacking fashion only to be rocked on their heels by Arca's third goal of the season.
Sunderland missed two great chances to increase their lead, Oster firing weakly at Provett who then made an instinctive save from Stewart's close range header.
Hartlepool boss Neale Cooper used all three substitutes in a 15-minute spell in an effort to force a replay and the move almost paid dividends as the Black Cats were forced to dig deep to survive.
Robinson failed to take advantage of a Phil Babb mistake, Westwood flashed a header across the face of goal and in a frantic finale Arca blocked from Clarke and Babb cleared off the line from Williams.
Cooper, disappointed not to have at least forced a replay, paid tribute to the fans for their tremendous support.
"To take 10,000 fans away in the early rounds of the Cup is phenomenal – I have never experienced anything like that in my life,'' he said.
"It was a great boost for the players and on their behalf I would like to thank the supporters. It's disappointing not to have got a draw or won but the players have to learn from the experience.''