The Anteaters (23-10) built a 12-point lead in the first half and extended it through the final 20 minutes. They advance to play No. 7 seed Cal Poly in a semifinal game Friday.
Russell Turner, the 2014 Big West Conference Coach of the Year has led UC Irvine to 10 wins in its last 11 games and 16 in their last 19.
UC Irvine used a 14-1 run in the first half to take control of the game, fashioning a 16-5 lead just eight minutes into the contest.
Davis was 6 of 10 from the field to finish with 16 points. Nelson was 5 of 10 for 14 points.
Nick Gruninger had 10 points for Riverside (10-21).