TCU (2-0) forced five turnovers and held Minnesota (2-1) to 99 yards rushing -- 134 below its average.
Doctson had a leaping grab with his right hand for a 7-yard score that increased TCU's lead to 17-0 early in the second quarter.
Trevone Boykin was 27 of 46 for 258 yards, two touchdowns and an interception. He also rushed 12 times for 92 yards.
TCU held David Cobb to 41 yards on 15 carries. Cobb averaged 145.5 yards rushing in Minnesota's previous two victories.
Doctson opened the scoring with a 13-yard over-the-shoulder catch. He finished with six catches for 64 yards.
TCU's newly-installed up-tempo offense wasted little time adding points on the scoreboard. Only one of the Horned Frogs' six scoring drives took longer than 2 minutes.
Minnesota's starting quarterback, Mitch Leidner, left the game early in the fourth quarter following a hard tackle. Leidner was 12 of 26 for 151 yards and three interceptions and also lost a fumble.
Leidner had just returned after leaving last week's Gophers win over Middle Tennessee State with a sprained ligament in his left knee.
TCU scored on its first two possessions and was never seriously threatened the rest of the way. After Doctson's first touchdown catch, the Frogs followed Minnesota's second consecutive three-and-out with the first of Jaden Oberkrom's three field goals, from 46 yards.
The Frogs' opening scoring drive of 18 yards was set up by a 46-yard punt return by Cameron Echols-Luper.
Midway through the first quarter, TCU had outgained Minnesota in total yardage 50 to minus-1. The Gophers finished the first quarter with minus-1 yard rushing.
Two of Minnesota's three first-half turnovers were turned into TCU touchdowns. Cobb lost a fumble on the first play after Boykin was intercepted by Briean Boddy-Calhoun at the Gophers 39.
TCU converted that into a 1-yard touchdown run by B.J. Catalon for a 24-0 lead with 9:01 to play in the half.
Minnesota had opened each of its previous two seasons with four consecutive non-conference wins.
TCU coach Gary Patterson and Minnesota coach Jerry Kill are long-time friends. Kill served in Patterson's wedding party 10 years ago. The home-and-home series will resume when TCU visits Minneapolis next September in the season opener for both schools.