Volquez, 33, struck out all three of the batters he faced in the ninth inning to complete the first no-hitter of the 2017 Major League Baseball season.
Jake Arrieta tossed the league's last no-hitter on April 21, 2016.
Volquez achieved the feat despite pitching with a heavy heart on what would have been the 26th birthday of his late friend and former teammate Yordano Ventura.
Kansas City Royals pitcher Ventura died after a car accident in their native Dominican Republic in January.
Volquez said he was thinking about his late friend during the game.
"I'm pretty sure he's in the right place right now, enjoying this moment right now," said Volquez, who dedicated his no-no to Ventura and Jose Fernandez, the Marlins pitcher from Cuba who died last year in a boating accident at the age of 24.
"I was pretty close to him in Kansas City for two years. He passed away, and it really hurt," Volquez said of Ventura. "It was special for me to dedicate the game to him."
Volquez finished with a total of 10 strikeouts to become the first Marlin to pitch a no-hitter since Henderson Alvarez on September 29, 2013.
The last time the Diamondbacks were held without a hit was by Marlins hurler Anibal Sanchez on September 6, 2006.
Volquez faced 27 batters, throwing 65 of his 98 pitches for strikes.
But he almost didn't make it out of the first inning. Volquez twisted his right when he Arizona's leadoff hitter Ray Fuentes as he raced to cover first base.
"I know Fuentes is really fast," Volquez said of his former teammate with the Royals and San Diego Padres. "It was a really close play. I hit the bag right in the middle, and my ankle twisted."
From there, Volquez said "it was just one of those days when you totally don't know what's going to happen."
Despite treatment between innings, including taping the ankle, Volquez said that even after he needed just 30 pitches in three perfect innings the pain was bad enough that he wasn't sure he'd be able to continue past the fourth.
"I had a quick inning and I told him just let me go, I feel better now," he said.
One of the biggest threats to Volquez's no-hitter came to lead off the fourth, when Marlins second baseman Dee Gordon made a diving stop on a sharp Fuentes ground ball.
"He saved the no-hitter right there," Volquez said.
On the next play, Volquez himself made a great grab on a sharp comebacker by David Peralta.
- Energy of the moment -
Despite his ankle trouble Volquez was in command all the way and the tension really mounted when he retired Diamondbacks slugger Paul Goldschmidt with a 92 mph (148.06 Km/h) fastball to end the seventh inning.
"Volquez starting feeling the energy of the crowd and the moment," Diamondbacks manager Torey Lovullo said.
Until that point the only D'Backs hitter to reach base was Jake Lamb, who walked to lead off the fifth before he falling victim to a double play.
After striking out Lamb to open the eighth, Volquez issued his second walk of the day to Chris Herrmann.
Herrmann, too was erased when Brandon Drury hit into a double play.
In the ninth Volquez struck out Nick Ahmed swinging with a changeup and also retired pinch-hitters Daniel Descalso and Chris Owings to the roars of the crowd.
Volquez, who hadn't pitched more than six innings all season, became the seventh pitcher from the Dominican Republic to throw a no-hitter and the first since Ervin Santana in 2011.
Marlins catcher J.T. Realmuto, who caught his first no-hitter as a pro, said he realized early in the game that Volquez was locked in.
"Around the second or third inning, I could tell his stuff was really good," Realmuto said. "I knew he had a chance to have a really good game."