Jalen Johnson and Hasahn French netted 12 points apiece for the Billikens, who snapped a four-game skid and evened their record at 4-4. French added a game-high four blocks.
Javon Bess had nine points and five rebounds, while Davell Roby and Aaron Hines chipped in eight points apiece. Hines led all players with a season-high seven assists.
Southern Illinois (4-3) saw its winning streak halted at two. Jonathan Wiley poured in a career-high 19 points and was joined in double figures by Armon Fletcher (12), Marcus Bartley (12), Sean Lloyd Jr. (11) and Kavion Pippen (10).
Saint Louis committed a season-low eight turnovers and earned a 30-27 rebounding edge that included an 18-11 advantage in the second half.
Southern Illinois led 57-52 with 8:21 remaining, but Saint Louis gradually pulled closer and tied it at 61 on a Bess 3-pointer at the 4:59 mark.
After French made a free throw for a one-point Billiken lead, Wiley sank two from the stripe to put SIU back on top.
French knotted the score at 63 with another free throw, and he gave Saint Louis the lead for good with a breakaway dunk following a steal by Bess.
Bess buried a trey for a 68-63 lead with 2:12 to play. A free throw and a bucket by Wiley drew SIU to within a field goal with 39 seconds left, but Hines and Goodwin converted two free throws apiece – with one of French’s four rejections in the middle – to stretch the margin to six, 72-66, with 19 seconds remaining.
Following a Saluki trey, Bess sank one at the line to make it a two-possession game with 10 seconds to play, and the Billiken defense did the rest.
SLU gained the upper hand with a 21-8 run over the next 9:12. Johnson scored seven points, Goodwin and Roby tallied five apiece, and French added four during the stretch, which resulted in a 30-26 Billiken advantage with 3:04 remaining.
SIU answered by outscoring Saint Louis 10-2 the rest of the half to carry a 36-32 edge to the locker room.
The Billikens host Houston Saturday, Dec. 9, at 7 p.m. The game will be carried on KPLR and Facebook Live.