Whoever wins Sunday will get to tee off at Augusta National next week.
The 38-year-old Herman shot a 5-under 67 Saturday to position himself for a breakthrough.
"There's a lot to play for tomorrow," said the pro from Cincinnati, whose best finish this season has been a 10th-place tie. "I had a couple of good par saves, especially on the last hole. I'm committed to going to the first tee (Sunday) and hitting that first fairway. I've got to ty to not put any extra pressure on myself."
Lovemark, 28 and a former NCAA champion at USC whose professional career was derailed by major back surgery, wasn't able to build on his fast start, which saw him birdie three of the first four holes. He stayed in the hunt with a 70 after opening rounds of 67 and 68.
"My confidence is good," Lovemark said. "I've got to keep doing what I've been doing. It's going to be a tough battle tomorrow. It'll be a shootout."
The Swede Stenson, No. 7 in the current world ranking, posted the day's best round with a 66 after also birdieing three of the first four holes. Henley had a 68 Saturday and Johnson a 70.
"The first two days I've hit the ball quite nicely but haven't been putting well," Stenson said, "so I worked again yesterday afternoon on that. I got it going a bit better today. I was more comfortable, found some lies and made a couple of beauties out there."
The 22-year-old Spieth, who stayed alive with three birdies on the back side, lost in a three-way playoff here last spring, then went on to win the Masters in resounding fashion, leading start to finish for his first major championship.
"I felt like I played well," said Spieth, who also won the 2015 U.S. Open but has struggled with his consistency over the last several weeks. "We had some unreal wind flips on the first six, seven holes, and we were on the wrong end of about six in a row. It's really tough to stay patient through that.
"I'm playing really, really solid golf. But it just hasn't come through in a (round of) minus 6 or minus 7. Hopefully that means we're saving them for tomorrow -- or next week."
Another shot back at 9 under was Roberto Castro, who also scored 70 and is trying to become the first Houston-born player to win the Houston tournament.
None of the leaders should be resting easily given the recent history of the event, which was founded in 1946. The last two champions here, Matt Jones in 2014 and J.B. Holmes a year ago, both came from six strokes behind starting the final round to claim the first-place check.
Nineteen players will tee off Sunday within six shots of the lead, including three-time Masters champion Phil Mickelson. Mickelson, also the 2011 Houston champion, had six birdies Saturday en route to a 71. A triple-bogey on the par-4 sixth hole kept him from being only three strokes off the lead.