McDowell carded five birdies in a bogey-free 66 on Sunday, but his momentum was stalled by two weather delays as heavy rain hit Robert Trent Jones Golf Club.
After a birdie on the 17th, the 45-year-old gave himself the chance to match Niemann's 15-under mark on the final green, but missed his putt on the left.
"I'm happy with the fight. It was tough to keep the momentum going with the breaks. I just asked Joaco [Niemann]'s caddie what they did in the second break because whatever they did was good," added the four-time Ryder Cup player.
"It's hard to play loose when you need it, when you kind of haven't been there for a while.
"But I was really happy the way I composed myself generally today. Drove the ball great. I felt pretty comfortable out there.
"Hopefully a big summer ahead, and like I said in the presser, [I've] been so disappointed with my general performance on LIV this to point, this is what I expect of myself still. Really nice to get the juices flowing a little bit. I'm super excited about the week."