Ruben Tejada's three-run homer -- his second of the spring -- off Brandon Beachy in the fifth inning was the big blow for the visitors.
Making his Spring Training debut after undergoing back surgery in November, Hudson said he felt "totally normal" in two innings of work. The 36-year-old right-hander faced seven batters and allowed only one hit, striking out two in the first inning and working a 1-2-3 second inning with three groundouts to shortstop Tyler Pastornicky. Of the 25 pitches Hudson threw, 16 went for strikes.
"Honestly, I went out there and tried to pitch like I was in a real game. I was trying to make pitches and get some swings and misses," he said. "I wasn't really trying to finesse around anything. At this point, I need to see where I'm at. And so far, so good."
Reliever Bobby Parnell threw three scoreless innings as the Mets' starter. The right-hander hasn't been touched for a run in 12 1/3 innings of work this spring, allowing only seven hits and two walks while striking out eight batters in Grapefruit League play.
"Everything felt great. I had a good two-seamer," Parnell said. "And they're probably ready to go up north, so they were swinging early."
The Mets scored first against Beachy, who followed up Hudson. Wilfredo Tovar led off the third inning with a double to right field, moved to third on a bunt by Parnell and scored on Tejada's double-play groundout.
Third baseman Juan Francisco, acquired Sunday in a trade with the Reds, made his Braves debut Monday. The big lefty hitter struck out looking in his first at-bat after working a 3-1 count and fouling off three straight pitches. He finished the day 0-for-4.
Up next: The Mets will wrap up Spring Training with a home-and-home series with the Yankees, starting Tuesday at 2:10 p.m. ET in Port St. Lucie. The game will be the first Florida meeting for the two New York clubs since 1996, and it can be seen live on MLB.TV. Right-hander Mike Pelfrey and lefty Jon Niese are scheduled to pitch against Yankees right-hander Ivan Nova.