The Aztecs (31-4) now get to make the short drive up the interstate to Anaheim, Calif., where they will face either No. 1 seed Arizona or eighth-seeded Gonzaga in the West Regional semifinals on Thursday.
Thames, who was 9 of 19 from the field, had five assists and ended the comeback hopes of the Bison with a six-point spurt late in the second half that pushed the Aztecs' lead to 12. He finished one shy of his career-high in points.
Dwayne Polee II was the only other San Diego State player in double figures with 15, but the Aztecs didn't need a ton of scoring with Thames carrying the load and another defensive performance that suffocated the best shooting team in the country.
Kory Brown led the Bison (26-7) with 13 points, but it was the struggles of leading scorer Taylor Braun that had North Dakota State trying to play catch up. Braun missed nine straight shots during one stretch. Sometimes he was guarded by Thames. Other times it was J.J. O'Brien taking a turn on the Summit League player of the year.
Braun finished 2-of-14 shooting and just seven points. North Dakota State shot 50.9 percent for the season to lead the country, but could only make 31.9 percent against the Aztecs. The 44 points were a season-low for the Bison, the previous low being 56 in a win over Western Illinois.
North Dakota State was one of three No. 12 seeds to help create another manic March by upsetting No. 5 seed Oklahoma 80-75 in overtime in the second round on Thursday. They had the players and the personality to become this year's version of FGCU just minus all those dunks.
Thames wasn't going to allow that to happen. The memories were still fresh of the flight home last year after San Diego State become one of those teams FGCU dunked all over on its way to an unforgettable March run.
Thames did it all for the Aztecs in the first half. He was responsible for 23 of San Diego State's 30 points, scoring 16 and assisting on another three baskets. He started the second half with a floater in the lane, a shot he repeated minutes later. He then found Polee on the wing for a 3 and the Aztecs lead was back to 40-30 after a quick North Dakota State spurt had trimmed the deficit to five.
Braun finally got a shot to fall when he spun in a reverse layup with 12:11 left, his first field goal in nearly 27 minutes of game time. By that point, the Bison were down eight and could never get much closer.
Braun finished the first half 1-of-10 shooting and equally quiet was Lawrence Alexander. The guard who hit all the big shots against Oklahoma finished with three points after scoring 28 against the Sooners.