Dixon had been following closely behind leader Will Power (Team Penske) before being able to take the lead when the Australian was delayed in the pits.
Both leaders remained glued to each other but Dixon took advantage of the fact that he made his last stop under a yellow; rejoining the race in third behind Power and Luca Filippi (Herta Motorsport), both of whom still had a stop to make.
After that, Dixon was able to create a gap over Simona de Silvestro (KV Racing) who had been running in the top 5 all afternoon.
The Kiwi was flying to the finish line when an incident involving Mike Conway with three laps to go, forced the race to finish under yellows.
Dixon's win along with the misfortunes of series' leader Helio Castroneves shrunk the Brazilian advantage from 49 points to only eight.
Castroneves was marred by a gearbox problem. He later lost more time to an array of minor incidents.
de Silvestro finished second, her first ever IndyCar podium followed by Dale Coyne's Justin Wilson.
Simon Pagenaud was fourth while Josef Newgarden (Sarah Fisher) completed the top five.
Race 1 results – Houston, Texas (IndyCar)
1 - Scott Dixon (Dallara DW12-Honda) - Ganassi - 90 laps
2 - Simona de Silvestro (Dallara DW12-Chevy) - KV - 0"878
3 - Justin Wilson (Dallara DW12-Honda) - Coyne - 2"143
4 - Simon Pagenaud (Dallara DW12-Honda) - Schmidt - 3"549
5 - Josef Newgarden (Dallara DW12-Honda) - Fisher - 4"229
6 - James Jakes (Dallara DW12-Honda) - Rahal - 5"461
7 - Graham Rahal (Dallara DW12-Honda) - Rahal - 6"098
8 - Sebastien Bourdais (Dallara DW12-Chevy) - Dragon - 6"894
9 - Ernesto Viso (Dallara DW12-Chevy) - Andretti - 8"187
10 - Luca Filippi (Dallara DW12-Honda) - Herta - 9"305
11 - Charlie Kimball (Dallara DW12-Honda) - Ganassi - 9"962
12 - Will Power (Dallara DW12-Chevy) - Penske - 10"645
13 - Marco Andretti (Dallara DW12-Chevy) - Andretti - 11"143
14 - Sebastian Saavedra (Dallara DW12-Chevy) - Dragon - 1 lap
15 - Dario Franchitti (Dallara DW12-Honda) - Ganassi - 1 lap
16 - Mike Conway (Dallara DW12-Honda) - Rahal - 5 laps
17 - Takuma Sato (Dallara DW12-Honda) - Foyt - 8 laps
18 - Helio Castroneves (Dallara DW12-Chevy) - Penske - 10 laps
Lap 63 - Oriol Servia
Lap 57 - Ryan Hunter Reay
Lap 34 - Tony Kanaan
Lap 32 - Tristan Vautier
Lap 30 - Ed Carpenter
Lap 1 - James Hinchcliffe