Hudson didn't allow a run in 4 2/3 innings and Russell Branyan hit his fifth home run of the spring, but Texas rallied for four runs off Gutierrez in the ninth to beat the Diamondbacks 6-4 on Monday.
It was the final game for Arizona at its new Salt River Fields spring training facility this season and the last game in Arizona for the Rangers, who flew out afterward for an exhibition game against Coastal Carolina University on Tuesday in Myrtle Beach, S.C.
Hudson gave up four hits, struck out four and walked two.
"I had a couple of rough ones in a row," he said, "so it felt good to have a good outing like that to end the spring and get going into the regular season."
The right-hander, who turned 24 on March 9, was 7-1 in 11 starts with a 1.69 ERA after coming to Arizona from the Chicago White Sox as part of the Edwin Jackson trade last year. He opens the year as Arizona's No. 2 starter behind Ian Kennedy. His first outing will be Saturday at Colorado.
Hudson's previous game was against Texas, too, and he wound up allowing seven runs on eight hits in 2 2/3 innings. He was given the option of throwing a minor league game rather than facing the Rangers again.
"I said, 'No, I'll go after them again,'" he said. "It's not a big deal. Everybody has those outings every once in a while. I just kind of push through it and go on to the next one."
Branyan's two-run shot was the only damage done to Texas starter Matt Harrison, who allowed four hits, struck out three and walked two in four innings.
"Other than the ball that the big King Kong hit, I thought Harry did a good job of minimizing damage," Rangers manager Ron Washington said. "It could have been worse than that but he settled down. He made pitches when he had to. He got outs when he needed the outs."
Branyan had a grand slam against the Rangers last Wednesday.
Gutierrez, 0-6 with a 5.08 ERA last season, gave up four runs on five hits in one-third of an inning. For the spring, he's 0-3 with an 11.70 ERA.
With Arizona struggling all spring, the problems weren't just with Gutierrez, obviously.
"We haven't pitched well overall," manager Kirk Gibson said. "We haven't shut people down when we need to, so we need to have some discussion on it."
The Diamondbacks' 11-25 spring record is the worst in baseball.
Before the game, Gibson announced that Armando Galarraga would be the team's fifth starter. The Rangers still have not said who their fifth starter will be, but the odds-on favorite is Alexi Ogando, scheduled to start against Coastal Carolina on Tuesday.
After that, the American League champions go to Austin, Texas, to face their Triple-A team in Round Rock before heading home to open their season Friday against Boston.