UNM (16-8-1, 6-3 Mountain West) took two of three in the series.
The Lobos were shutting out the Spartans (7-18, 4-8) for eight innings before running into some trouble, most of their own making, in the ninth inning.
Overall, though, it was a nice rebound from Saturday's 8-5 loss as UNM jumped out to a 5-0 lead in the first three innings, highlighted by Harris' home run in the first.
"That's exactly how we needed to come out," Harris said. "I'm glad I could come out and get it started for us. But we knew having Walker up on the bump was going to be great for us."
Walker (3-1) went eight-plus innings, not allowing a run until he was charged with three in the ninth. All told, the senior scattered nine hits and struck out two batters, though he did allow his first two walks of the season.
Mike Simonini drew a full-count walk with two outs in the third inning, while Matt Lopez did the same in the fourth. Neither walk came back to haunt Walker, however, as he got the next two batters on a groundout and a flyout, respectively.
"It was fine, (but) I was trying to do too much in the beginning," Walker said. "But it was good to get some zeroes up there and score early. It's a good bounce-back from (Saturday).
"Walks are going to happen sometimes. It's not a big deal as long as we're winning."
The Lobos gave Walker plenty of run support early on. Following Harris' home run in the first, Danny Collier had an RBI single and Harris added a sacrifice fly to make it 4-0 in the second. Jared Holley would add an RBI double in the third.
"It took a lot of pressure off us, I think, getting a couple runs up there on the board in the first inning," Harris said.
UNM tacked on three more runs in the seventh and one in the eighth. Harris and Collier both finished with three hits, while Andre Vigil went 2-for-4 with two RBI.
San Jose State did pick up those four runs in the ninth, taking an advantage of an error and some additional miscues. Harris said those mistakes should not stay with the Lobos in the future.
"I feel like maybe we let up a little bit there at the end, but luckily we had the lead we did and we won't let that happen again, either," Harris said.
There was a small scare in the fifth inning when Holley came up lame after reaching first base on an error by Spartans third baseman Jacob Valdez. He was removed from the game in the sixth, with Sam Haggerty shifting from second base to shortstop and Jered Meek taking over at second.
"Holley pulled a hamstring, it's (just) a twinge," coach Ray Birmingham said. "We've got some hamstring problems. (Alex) Real played the whole game with a hamstring problem. Holley tried to go as long as he could."
The Lobos will hit the road for their next five games, starting Tuesday at New Mexico State. The next home game is April 2 against the Aggies.