Power got to within a shot of the early lead on two-under-par after making three birdies and a bogey on the front nine but dropped three shots in a row from the 10th en route to a 71 that left him tied 42nd, five shots behind leader Adam Hadwin of Canada on one-over par.
Lowry turned in one-under thanks to a birdie at the eighth and some good par saves, but playing with out-of-sorts LIV Golf rebels Phil Mickelson and Louis Oosthuizen, who struggled to rounds of 78 and 77, respectively, he dropped shots at the 11th, 12th and 16th to lie tied 57th after a two-over 72.
"I am a bit frustrated; I think I played good enough to shoot par or better," said Lowry, who lost 1.22 strokes to the field on the greens and more than five and a half strokes to Rory McIlroy, who had his best putting round on the PGA Tour since 2015.
"It was hard out there, the wind was up, the course was tough, and you needed to be in position a lot of the time, which I was," Lowry added.
He bogeyed the 121-yard 11th when he came up short in a bunker, then missed the 12th green from the middle of the fairway before failing to convert a short putt at the 16th.
"I had it going lovely and then 11 was a bit of a kick in the teeth, to be honest. It was silly by me and then 12, middle of the fairway and you make bogey there and all of a sudden, you feel like you are holding on on the way in.
"On 16, I probably should have hit eight iron, but I hit seven iron over the back and missed a short putt, hit a great drive on 17 and didn't make birdie there, and I feel like I scored really badly.
"Even though I had a couple of good up and downs, I feel like two-over is probably one of the worse scores I could have shot. I don't have much time but get some food and get ready to go again tomorrow.
"Hopefully, I can go out and break par tomorrow and then I will be back in it because I don't know what it is going to take to win this tournament, but it is not going to be much, scoring-wise.
"There is going to be a lot of good golf, but it is hard out there. I don't know what the forecast is tomorrow, but if it is as windy as this, it is going to be a pretty high cut."
Lowry goes off at 8.02am local time and he's hoping calmer conditions will allow him to break par and stick to his game plan.
"I will go out and try and break 70, give it my best and do what I am doing, keep hitting shots and try and shoot the best score," he said.
"I hit a couple of clubs off tees that I wasn't planning on doing, on five and 17, I was planning on laying up, but it was just playing so hard you have to get it as close to the green as you can, so I was more aggressive there.
"I feel like with the golf I am playing, if I can roll a few putts in, I can shoot a good score out there. Hopefully, that comes tomorrow. If it does, it does. If it doesn't, it doesn't. I will give it my best."
As for the lack of energy in the group in a slow back nine, he said: "They struggled; I was focused on myself. They didn't have the best day, both of them, it is hard out there, when you are hitting a few wayward shots, it is really, really hard.
"The course is excellent, as good a set-up as I have ever seen. You can hit it in the rough and still have a shot at the green. It is not like Winged Foot. I think they have got the course spot on."
Power was pleased with his 71 and might have matched par or even shot under had some long birdie putts at the 13th, 15th and 17th not lipped out or missed narrowly.
But he was also grateful to hit the pin at the last and save par after short-siding himself right of the green when his wedge from the right rough came out flying.
"I'd say I probably scored what I deserved," said Power, who was not helped by the fact his group, with Joohyung Kim and Min Woo Lee, were on the clock from the seventh.
"I played nicely on the front and there was a couple of loose shots on the back. I know it's my first US Open, but anything loose and you were in trouble.
"I had a couple of long putts that almost dropped but overall relatively pleased."
After finishing tied 27th in the Masters and tied ninth in the USPGA, the West Waterford man put his excellent start to his Major career down to his amateur days.
"Yeah, I think growing up playing a lot of links golf in tough conditions, you know par is a good score and that's what I've seen so far in majors this year and certainly in the three I've played it's been that way," he said.
"Anything around par is good and we had a lot of practice and that playing in Rosses Point when Easter was early and that sort of thing.
"I think some of those skills don't go away and you manage to get around as close to par as you can. And weeks like this, you're really looking for one or two good streaks and then holding on for the rest of it. So, hopefully, I can get one of those streaks tomorrow and see where it goes."
Happy with his score, he added: "It's tough this afternoon with the wind. You could shoot yourself out of the tournament, which I feel like I haven't done, so that's certainly a positive. You'd like to see it in the red figures after the first day, especially in round one. Overall I didn't quite play my best, but I was able to hang in there."
Canadian Hadwin, who was an alternate earlier in the week, set the pace with a four-under 66 to lead by a shot from a five-man chasing posse featuring Rory McIlroy, English qualifier Callum Tarren, Sweden's David Lingmerth, Joel Dahmen and the South African MJ Daffue on 67.
Matt Fitzpatrick, Dustin Johnson and Justin Rose were in a seven-man group on two-under after 68s on a day when 25 players broke par.