Harden, in his Texas debut, pitched two innings of one-hit ball and Saltalamacchia and Matt Brown each hit a three-run homer, leading the Rangers to a 13-3 win over the Kansas City Royals on Thursday.
The Rangers pounded five KC pitchers for 21 hits in the spring opener for both clubs. Mitch Moreland was 3 for 3 with two RBIs.
Harden, who spent the past 1½ years with the Chicago Cubs, had one walk and one strikeout and gave up one unearned run.
"Rich looked great," said Saltalamacchia, the Rangers' catcher. "He was throwing all his pitches with command, which is big, and he was just working on things. He looked comfortable. I could call anything at any time."
In another good sign for Harden, the right-hander had little trouble getting ground balls from the Royals, who managed only six hits off six Texas pitchers.
"Overall, I was pretty happy with the way it went," said Harden, who is expected to be the Rangers' Opening Day starter. "First time out, just getting comfortable out there. The key for me is to try to get ahead and throw first-pitch strikes. I got a lot of grounds balls today, and that's what I want to do."
Davies got through the first inning with only one baserunner before the Rangers sent eight men to the plate in the second. Nelson Cruz singled and Chris Davis walked before Saltalamacchia worked the count to 2-2 and slammed the next pitch over the fence. Julio Borbon doubled and made it 4-0 on Michael Young's single.
"We haven't played in a while, so to get out there and get all the kinks out is great," said Saltalamacchia. "But to start off like that is always good. You get a little confidence."
Davies was charged with four runs on five hits. Robinson Tejeda, trying to make the transition from reliever to starter, didn't fare much better. He gave up four hits and two runs.
Billy Butler had one hit in two at-bats for the Royals, striking out on a changeup in the first inning.
"Rich Harden has been around for a while," he said. "I want to see the best to get you ready for the first game. I don't care who is out there. The better pitchers are always better for seeing good pitches."
Brown connected off Matt Herges in the Rangers' four-run ninth.
Harden was also pleased to make a good first impression with his new team.
"Yeah, but you don't want to go out there and change what you do just because of that," he said. "But, yeah, being with the new team, I want to go out there and pitch well for them. But I've been around long enough to realize this is just spring, a time to get ready. And good or bad, you can't win championships in spring. It's a time to work on things."