Shippen, a 6-foot, 175-pound senior guard, sparked the Rams, who rebounded from a lopsided loss to Lower Merion in a Central League playoff semifinal, with a game-high 29 points as well as seven rebounds and three steals.
"There was no shame in losing to Lower Merion," Shippen said. "We still had a lot of confidence coming into districts. We believed in ourselves."
The 5-11, 155-pound Dixon, a senior combination guard, posted 13 of his 18 points in the last 16 minutes. He added four boards and three assists.
"We got off to a slow start," Dixon said. "Once we settled in on defense, packing it in and fronting their big men, that turned things around."
Next for No. 20 seed Harriton (15-9) is a second-round matchup against the survivor of Saturday's contest between No. 29 Kennett and No. 4 Spring-Ford.
"Our whole thing was, we didn't want to say goodbye," Rams coach Jesse Rappaport said. "I told our kids before the game, 'The story can't end here.' "
Shippen shot 7 for 12 from the field (4 for 4 from beyond the arc) and 11 for 14 from the foul line. In the first round last season, his last-second shot produced a 53-51 win over Council Rock North.
Dixon, whose nose was bloodied by an elbow in the second quarter, was 6 for 11 from the field and 6 for 10 from the stripe.
Overall, Harriton went 24 for 34 from the line. The visitors forced 13th-seeded Coatesville (14-10) into 16 turnovers.
Wright, the squad's sixth man, contributed 16 points, including a pair of second-quarter threes.
"He's great at giving us a spark when we need it," Shippen said.
For the Red Raiders, Tyler Burke, who will play football at Maryland, managed 16 points and 12 boards. Their other 6-4 senior forward, Jaquan Hollingshed, was slowed by foul trouble and finished with eight points.
Harriton 8 20 24 21 – 73
Coatesville 13 21 14 12 – 60
H: Detasla Dixon 18, Alex Shippen 29, Sam Schlichting 5, Spencer Dickler 5, Jordan Wright 16.
C: Kevin Crutchfield 2, Jaquan Hollingshed 8, Tyler Burke 16, Keenan Coleman 13, Ricky Southcott 6, Calvin Young 9, John Rodriguez 5, Amir Ealey 1.