Hudson (7-1) has now won his past four decisions and has not suffered a loss since Aug. 17, a span of seven starts. He carried a one-hitter into the ninth inning and came within one out of a complete game.
After retiring the first two hitters in the ninth, Hudson gave up a single to Ryan Theriot on a shot that snuck past the glove of Adam LaRoche at first.
Interim manager Kirk Gibson decided to give Hudson another chance to finish things, but he ended up taking him out when he walked Andre Ethier.
"He pitched good," Gibson said. "Of course he wanted to go the full game and I wasn't willing to do that. There'll be another day for that."
Spent from the effort, Hudson did not argue when Gibson sprinted out of the dugout to remove him.
"I was actually expecting him to come get me after that first guy, but he gave me one more batter and I didn't get him out," said Hudson, who threw 112 pitches, 70 for strikes. "Obviously, getting into the ninth for my first time in my career, I'd like to finish it. I was probably one pitch away from finishing it."
With as well as he pitched, it is hard to believe that Hudson was actually behind by a run heading into the bottom of the fifth inning.
The lone hit he had given up to that point was a ground-rule double to left-center by Trent Oeltjen. Theriot's sac bunt moved Oeltjen to third and he scored on Ethier's groundout to give L.A. the lead.
"The Dodgers were really aggressive early in the game. I saw that and kind of wanted to play to that -- throw a lot of strikes and let them get themselves out," Hudson said. "I think that helped my pitch count out a lot."
To that point in the game, the D-backs had been able to put runners on base against John Ely -- they just were not able to get them across the plate. Arizona stranded six runners through the first four innings.
Finally, in the fifth, the D-backs broke through. Stephen Drew led off with a triple and scored on Tony Abreu's sacrifice fly to tie things up.
One inning later, Cole Gillespie broke the game open when he hit a three-run homer to left to give the D-backs a 4-1 lead. The homer came after the Dodgers elected to intentionally walk Brandon Allen to put runners on first and second.
"You'd like to make them feel like it's a bad decision," Gillespie said. "A little more incentive I guess to come through in that situation. You always want to come through with guys in scoring position, but when they intentionally walk the guy in front of you, you kind of like to make it backfire on them."
The D-backs tacked on another run in the seventh, and by that time, the biggest question was whether Hudson would get the complete game.
The slider is admittedly Hudson's third-best pitch, but it turned out to be a real weapon for him.
"It was a good pitch for me tonight, especially with some of their righties in there kind of aggressive at the beginning of the game, so I kind of got some awkward swings on them," Hudson said. "There at the end, I was pretty much going fastball-changeup."
Hudson has one more start left this year, and he doesn't want to stop given the roll he's on. Yet he also is aware of the fact that this is the first time he's pitched in September during his career.
"It's the end of the season, and I can tell," he said. "My body is just about done. I think it will be good to get some rest in the offseason."