Mitchell connected on 7-of-9 from the field and the Billikens (27-6) used a tough defense to hold their opponent to 33.9 percent shooting in claiming the A-10's automatic NCAA Tournament bid.
Dwayne Evans contributed 16 points and eight rebounds for top-seeded Saint Louis, which reeled off its 15th win in 16 games to take its first conference tourney crown since 2000 when it was in Conference USA.
The Billikens improved to 24-3 since the Dec. 1 death of former head Coach Rick Majerus.
Second-seeded VCU (26-8) was led by Treveon Graham with 20 points and 12 rebounds.
Juvonte Reddic supplied 15 and eight for the Rams.