Tate, a native of Starkville, turned in a time of 45.74, the fifth fastest of the afternoon, while Jamaica's Muir crossed the finish line seventh at 53.04.
The finals are set to begin at 8:25 p.m. CT Friday.
"Tavaris came into the college scene with a lot of expectations on his shoulders, and people don't understand how much pressure is on him to succeed," 22nd-year MSU coach Al Schmidt said. "But he's going out Friday to win this thing, and he can do it. I've been so proud of what he's been able to do. Jody has gotten better every time she's stepped out on the track. There's no question these two are stars of the future if they continue to progress the way they've been."
It was also an outstanding day for upperclassmen LaQuinta Aaron and junior Emanuel Mayers.
Aaron opened competition in the heptathlon with a second-place finish in the 100-meter hurdles at 13.67 and enters Thursday's final three events tied for 14th with 3,213 points, just 18 off the pace she had after Day 1 of the SEC Championships, where she finished with a career-best 5,633 points.
She put herself into the position she's in by matching her season-best in the high jump at 5-00.5, while finishing 7th in the 200m at 25.0.
"If she equals what she did on Day 2 at the SECs, she'll have a phenomenal day," Schmidt said. "If she has that type of performance, she'll be an All-American."
Mayers closed out Mississippi State's action on Wednesday in grand fashion, finishing sixth overall in the 400-meter hurdles at 50.36 to advance to Friday's finals.
It was the type of performance Schmidt described as "rock solid."
"He's been so strong for us all year," Schmidt said. "If he gets the right lane, he's got a chance to give us some good points."
The day, however, wasn't without disappointment.
The 4x100 SEC championship fourseome of Justin Christian, Kendall May, Dwight Mullings and Tate failed to qualify after May reinjured a hamstring on the backstretch with the Bulldogs leading their heat. The injury also knocked May out of the semifinals of the 100-yard dash.
Then there were O'Neal Wilder and Mullings just missing out on qualifying for the finals of the 400, as was the case for Crystal Wilson on the women's side.
"I really hate it for them," a disappointed Schmidt said. "They'd work so hard to get here. But we've got to put it behind us and move on. We still have a chance for a great finish."
Action resumes on Thursday with Aaron wrapping up the heptathon and the men's and women's 4x400-meter relays.