The action started when polesitter Ryan Hunter-Reay showed a bit of impatience while trying to pass Josef Newgarden as he exited the pits with cold tires.
The Andretti Autosport driver tried to sideline Newgarden with an ill-conceived lunge at Turn 4, only to clatter into the Sarah Fisher Hartmann car and bounce off the wall.
His teammate James Hinchcliffe had nowhere to go but into the wreckage, triggering a chain reaction that also accounted for Jack Hawksworth, Tony Kanaan and Takuma Sato.
Many drivers were able to get through the traffic jam but Helio Castroneves, who at first was able to avoid the accident, was clipped by Hunter-Reay's car as it bounced across the track.
Other drivers would have their share of problems as Simon Pagenaud was hit by Will Power mid-race and Sebastien Bourdais did the same on his own by making two trips into the wall that put him out of contention.
Scott Dixon took the lead in the latter stage of the event but was running low on fuel and had to make a 'splash & go' in the pits but not before putting Justin Wilson, who was running second, into the wall when the pair accidentally made contact on a late restart.
Conway took over the lead and kept Will Power at bay for the final two laps to secure the win.
Rookie Carlos Munoz claimed third ahead of Juan Pablo Montoya and Simon Pagenaud.
Race results - 80 laps:
Pos Driver Team/Engine Time/Gap
1. Mike Conway Carpenter/Chevy 1h54m41.6418s
2. Will Power Penske/Chevy +0.9005s
3. Carlos Munoz Andretti/Honda +1.5591s
4. Juan Pablo Montoya Penske/Chevy +2.0226s
5. Simon Pagenaud Schmidt/Honda +2.8169s
6. Mikhail Aleshin Schmidt/Honda +3.8574s
7. Oriol Servia Rahal/Honda +4.9621s
8. Marco Andretti Andretti/Honda +8.1948s
9. Sebastian Saavedra KV/Chevy +8.9029s
10. Carlos Huertas Coyne/Honda +24.2295s
11. Helio Castroneves Penske/Chevy +30.0552s
12. Scott Dixon Ganassi/Chevy +30.7310s
13. Graham Rahal Rahal/Honda +1 lap
14. Sebastien Bourdais KV/Chevy +3 laps
15. Jack Hawksworth Herta/Honda +3 laps
Justin Wilson Coyne/Honda 64 laps
Ryan Briscoe Ganassi/Chevy 60 laps
Tony Kanaan Ganassi/Chevy 55 laps
Josef Newgarden Fisher/Honda 55 laps
Ryan Hunter-Reay Andretti/Honda 55 laps
James Hinchcliffe Andretti/Honda 55 laps
Takuma Sato Foyt/Honda 55 laps
Charlie Kimball Ganassi/Chevy 41 laps