It was Dixon's first Indy 500 victory and the second Indy 500 win for team owner Chip Ganassi.
He led the race 115 of its 200 laps, but a solid final pit stop secured the victory.
"What a day," he said in a post-race television interview. "You just thought something was going to go wrong. What a day. We had a good car. We just had to stay ahead of those other cars."
Dixon was in second place, but his crew took only seven seconds at the final pit to give him the chance to beat Meira to the checkered flag.