The Texans selected Stanford defensive back Justin Reid with the 68th overall pick. With the 80th pick, the Texans selected tackle Martinas Rankin. And at the 89th pick, the team selected Jordan Akins, a tight end out of Central Florida.
At the Texans 103rd pick, the team selected wide receiver Keke Coutee on Saturday.
The Texans had no picks in the first round Thursday night and none in the second round, either - the first time that has happened in franchise history.
With the trio of picks in the third round, the team fulfilled needs on the offensive line, at tight end and in the secondary.
Staying home in the city of Houston, the Texans selected defensive end Duke Ejiofor in the sixth round.
FULL LIST OF TEXANS DRAFT PICKS:
3rd Round: Justin Reid, S, Stanford
Martinas Rankin, OL, Mississippi State
Jordan Akins, TE, UCF
4th Round: Keke Coutee, WR, Texas Tech
6th Round: Duke Ejiofor, DE, Wake Forest
7th Round: Jermaine Kelley, CB, San Jose St.
Texans' J.J. Watt offers advice for incoming rookies on draft night
JJ Watt gives advice about incoming rookies on NFL Draft night
The Associated Press contributed to this story.