At the time Mark Winterbottom was leading but he was passed by Coulthard with just three laps remaining after a restart and the New Zealander claimed the win.
Coulthard's victory was his second in consecutive days after he broke through for his first championship race win on Saturday on the back of three-non championship victories at the Melbourne Grand Prix meeting.
It came with a panel-banging move on Winterbottom at turn four which left the Ford driver crossing the line in second place with a flapping front guard.
"There were a few times I could have had a go at Frosty (Winterbottom) early in the race but he moved more than once in the braking area which makes it hard," Coulthard said.
"I had my opportunity and I admit the left front did lock up and I did run a little bit wide but we're here to race and it was hard but I thought it was pretty fair."
Earlier, Jason Bright drove his Brad Jones Racing Holden to victory in the 42-lap first race of the day, winning by 3.5 seconds from Holden Racing Team's Garth Tander.
But the series points table is still led by Red Bull Racing's Jamie Whincup, who finished fifth in the last race, ahead of Ford's Will Davison.
Bright's win was his first V8 Supercar race success in two years.
"It's been too long again," Bright said. "I seem to be putting long breaks in between my wins.
"But the car has come out of the box strong and hopefully it will continue for the rest of the year."
There was early drama in Sunday's first race when David Reynolds' Falcon was slammed into a rail guarding the wall on lap two.
At the exit of the hairpin, Reynolds, David Wall and the Nissan of Michael Caruso were three wide and Reynolds was left with no room.
The impact ripped the front suspension from his Ford but Reynolds was unhurt.
"I ended up hitting two walls for the first time ever," Reynolds joked later.
Red Bull Racing's Craig Lowndes, who is chasing the all-time touring car race win record, continued to have a miserable weekend.
Lowndes qualified off the pace and took his Holden home in 10th place and followed with an 11th in the last race.