Sikeston, seeded second, raced out to an early lead and never looked back against the seventh-seeded Dons (7-10).
The Bulldogs (18-6) play sixth-seeded Perryville today at 2 p.m. The Pirates upset No. 3 Notre Dame 9-5.
Doniphan actually led 1-0 in the top of the first inning on an RBI-single by Newman to bring in Charles Wilson.
Sikeston responded with five runs in the bottom of the first inning to take the lead for good.
Gilliland went 2-3 with three RBIs.
"As a team we hit up and down the lineup," Sikeston coach Kevin Self said. "And there were a lot of balls we hit hard but they were right at them. I thought their pitching wasn't too bad. They threw everything they had at us but we were able to hit some balls hard and build on our lead."
The Bulldogs led by as much as 9-1 in the bottom of the sixth inning. Doniphan tacked on one final run in the top of the seventh to reach the final margin.
"This district is always tough," said Doniphan coach John-Marc Merriman. "Anybody around here will tell you -- Dexter, Sikeston Cape Notre Dame -- this district is the toughest one to play in. We're a smaller 3A compared to these teams and it's tough."
Doniphan never could solve junior hurler Garrett Limbaugh, who picked up the win in seven innings of work. He allowed four hits while striking out six and walking one.
"He threw strikes, that's the main thing," said Self. "He made them hit it and for the most part we fielded it. He did exactly what I thought he could do. His fastball moves a little bit -- it's a little different. So if you've never faced him before, he's got the advantage."
Merriman said: "We never could get caught up. He kept us off balance. He worked the zone on us. We're used to seeing different pitching with the smaller schools we play. When you get over here it's just tough competition."
Sikeston chased Doniphan starter Newman in the first inning. The sophomore right-hander faced just nine batters, but Merriman saw his pitcher getting frustrated after allowing five runs in the first inning.
"I did pull him early. I didn't want to get too deep in the hole than what we already were," said Merriman.
Wilson led the Dons with two hits.
Sikeston was led by Scott Droddy (2-4, two runs), Baker (2-3, two runs, two RBIs) and the aforementioned Gilliland.
The Bulldogs collected 11 hits as a team.
Sikeston has not lost a first round district game since the 1999 season, which is the only time it's happened in Self's 11 years as head coach.
WP - Garrett Limbaugh. LP - Newman. HR - Seth Baker (S). 2B - Freddie Gilliland 2 (S), Josh Jackson (S). Multiple hitters - Sikeston: Scott Droddy 2-4. Baker 2-3. Gilliland 2-3. Doniphan: Charles Wilson 2-3. Records - Sikeston 18-6. Doniphan 7-10.