Martin was impressive in the perfect ninth inning, needing just 10 pitches to retire the Diamondbacks in order.
He is the first full-time position player to work a 1-2-3 ninth inning for a winning team since at least 1925 according to MLB.com.
Martin was able to get back-to-back groundouts from Ketel Marte and Nich Ahmed, and then got John Ryan Murphy to fly out to center to end the game.
The catcher is the first position player to close out a win since Detroit Tigers left fielder Willie Smith did it in September 1963 in a 4-1 win over the Washington Senators. Smith made 29 total pitching appearances over his career.
The 36-year-old said after the win that he had not pitched in a game in nearly 20 years, but was able to convince manager Dave Roberts to give him the chance with the Dodgers leading by 13 runs in the ninth inning.
The fastest pitch that Martin threw was measured with a velocity of 83.7 miles per hour.
"It's not really a slider, it's not really a curveball," Martin said to the LA Times.
"It's an in-betweener, but I want to know what my spin rate is like. Everyone's talking about spin rate. I wonder if I had a good spin rate."
Roberts gave credit to his catcher after the game, also joking that he was better than his other pitchers thus far a few games into the season.
"He was our most effective pitcher these three games," Roberts said.
.@russellmartin55, don't forget to shake Barnesy's hand.