A monster accident involving Vicky Piria, William Buller and Robert Cregan brought the safety car out for seven laps.
On the restart Evans out-braked Abt to gain the lead and set about clicking off fastest laps until another accident caused the race to finish under caution to give Evans his third race win of the season.
"It wasn't a great start from myself, I got a lot of wheel spin and Daniel got me straight away. I was a bit annoyed about that but I just put my head down and got on with it.
"Daniel left the door open so I just made a move - as that might be my last opportunity - and it paid off."
Evans now heads to the Hungaroring, Budapest for round six of the championship next weekend.
Dixon struggles
New Zealand driver Scott Dixon's IndyCar season continues to test the patience of a saint.
After a lacklustre qualifying and a 10-grid penalty for an engine change, which saw him start the race from 18th on the grid, his day was always going to be hard.
Starting that far back in a quality field is handicap enough, but it looked good for the Target Chip Ganassi Racing driver when he posted the fastest lap during the last practice session.
But just as the race was settling down, Dixon's car wouldn't play ball. On lap five Dixon's car would fall into neutral during the heavy braking zones and then the car developed a problem with its anti-stall, which really hurt his race prospects.
"These things really hurt us especially because the race didn't have any yellows," said Dixon.
"When you start that far back like we did, you need to work on fuel mileage and take some chances but we just couldn't really go anywhere."
Helio Castroneves denied Takuma Sato his maiden IndyCar victory in a close race, which was run under full green the whole way around the Canadian Edmonton airport circuit.