Zimmermann was upset after getting grazed on the elbow by a pitch in the second inning.
"When he's throwing at you, it kind of makes you a mad a little bit, and frustrated," Zimmermann said. "Just throw it over the middle. You have good control. It's not like he's wild. He's always around the zone.
"I don't know if it was intentional or not, but it sure seemed like it," he said.
Alvarez, speaking through a team translator, said hitting Zimmermann was an accident.
"It was a sinker that got away," Alvarez said. "It was two outs. The pitcher's up at bat. It was not something I did intentionally. It was just a pitch that got away from me."
Alvarez appeared to be expecting retribution when he came to bat leading off the third. He backed away from Zimmermann's first pitch before eventually grounding out to second.
When Alvarez came to bat again in the fifth inning, there were runners on first and third with no outs. Alvarez squared to bunt and Zimmermann threw a low, inside fastball that had the Marlins pitcher falling to the dirt to avoid it.
Zimmermann said he threw the pitch to try to induce Alvarez to pop up the bunt.
"I thought Zimmermann's was intentional, just kind of returning the message," Alvarez said.
After bunting on the next pitch, Alvarez glared at Zimmermann as he headed back to the Marlins dugout.
"He stared me down and I turned around and said, 'Can I help you?' Zimmermann said. "He didn't say anything and I said, 'Get back to the dugout where you belong.'"
Nationals manager Matt Williams said, "Boys will be boys. Into spring training, everybody's a little testy."
Alvarez, who is projected to be the Marlins opening-day starter with Jose Fernandez recovering from Tommy John surgery, gave up all four runs in the third inning.
Nationals: Zimmermann gave up a run following a leadoff triple by Miami's Dee Gordon in the first inning, but worked his way out of some later jams and shut the Marlins out the rest of the way. He went five innings. After throwing 63 pitches, Zimmermann went to the bullpen and threw 10 more. He declared himself "pretty close to ready" for the start of the season.
Marlins: Alvarez also went five innings and ran into trouble in the fourth when he said his fastball was getting up in the zone. Washington's Wilson Ramos hit a two-run single and Dan Uggla smacked a two-run homer against Alvarez in that inning.
Nationals: 2B Yunel Escobar (strained left oblique) went through a full workout Saturday and will do so again Sunday. If all goes well, he will make his spring training debut Monday against the New York Yankees. ... Jayson Werth (right shoulder surgery) felt fine after playing defensively in a minor league game Friday. ... Werth got the day off Saturday, but will play again on the minor league side Sunday. Asked if it's possible Werth could still be ready for opening day, Williams said the team is being cautious with Werth, but "I wouldn't put it past him."
Nationals outfielder Tony Gwynn Jr. continues to make a case to stick with the team for opening day. He threw out two Marlins at second base and is batting .364 this spring.
Nationals: will travel to Lakeland where Washington's A.J. Cole will face Detroit's Justin Verlander.
Marlins: is home against Minnesota. Jared Cosart will pitch for Miami.