NSW State of Origin halfback Mitchell Moses nailed the winning field goal with five minutes remaining on Sunday to send Eels fans into raptures at Commbank Stadium.
Moses also slotted a sideline conversion only eight minutes earlier to tie the scores after a spectacular try to Parramatta captain and Blues teammate Clint Gutherson.
The airborne fullback somehow managed to plant the ball in the left corner before sprawling into touch, leaving Moses to set up the grandstand finish.
"Crazy game of footy," Arthur said.
Titans halfback Tanah Boyd had the chance to send the thrilling match into extra time but missed a field goal attempt from in front of the posts as the clock wound down.
With Gutherson, Moses and prop Reegan Campbell-Gillard all back and firing after missing last week's 46-10 belting from the Warriors, Parramatta were in control before being reduced to 11 men late in the first half.
First, winger Maika Sivo was sin-binned for a high tackle on centre Jojo Fifita, then Campbell-Gillard joined him after kneeing Gold Coast front-rower Chris Randall in the back.
Both players were placed on report and will come under the scrutiny of the match review committee.
From 12-4 down, the Titans cashed in to hit the lead through two electrifying tries to wingers Phillip Sami, the 50th of his career, and Alofiana Khan-Pereira, his 17th of a breakout rookie season.
A Moses penalty goal locked the scores back up again before Boyd replied to give the Titans an unlikely 16-14 halftime lead.
Bryce Cartwright briefly put Parramatta back in front when he scrambled over early in the second half, only for Boyd to stroll through under the posts to regain the lead for Gold Coast.
Back from his heroics for the Blues last Wednesday night, Campbell-Gillard had crashed over for the first try of the game before Will Penisini crossed to earn the Eels a 12-0 lead after as many minutes.
But Khan-Pereira's first try of a double revived Gold Coast's hopes before the game took its wild late twist.
"It's hard to win an NRL game and we did it with 11 players," Arthur said.
"It's hard. Every now and then you practice a bit of 12-men stuff, but not 11.
"So I'm extremely proud of them. There were plenty of things I could be critical of but I just want to focus on how we won a tight game and it's going to be crucial come the back end of the year."
A sixth win from their past seven games left Parramatta in seventh spot at the conclusion of round 20.
The Titans remain 12th but have fallen four points behind eighth-placed South Sydney following a third defeat by four points or less in as many weeks.
"If we didn't have bad luck at the moment, we'd have no luck at all," rued caretaker coach Jim Lenihan, who conceded the Titans probably need to win seven of their last eight games to make the finals.
