The top seed in the tournament for the seventh straight season, the Bearcats were dominant from the outset, leading by as many as 29 points in the first half.
Logan, the Conference Player of the Year, netted 13 points in the opening 20 minutes, when Cincinnati (28-3) opened a 47-23 lead.
Jamaal Davis added 13 points for the Bearcats, who will meet Charlotte in Friday's semifinals. Charlotte downed Tulane, 78-69.
Altron Jackson scored 21 points for South Florida (19-12), which beat Alabama-Birmingham in the first round on Wednesday. The Bulls likely will have to settle for a berth in the National Invitation Tournament.
The other semifinal was set earlier in the day when Marquette held on for an 84-76 victory over Louisville and Houstno surprised Memphis, 80-74.
Diminutive point guard Cordell Henry scored 24 points Thursday to pace Marquette and produce an outcome that likely will keep the Cardinals and Coach Rick Pitino out of the NCAA tourney.
Dwyane Wade added six of his 11 points during a key second-half stretch, helping the Golden Eagles (24-6) to a three-game sweep of Louisville (18-12) this season.
Louisville had won three straight games following a 6-9 stretch, but in Pitino's first year with the school, an NIT is the best it can hope for.
"If we get an NIT bid, we will gladly accept it and help our program grow," said Pitino, who won a national championship with Kentucky and has been to three Final Fours.
Marquette is a cinch for the NCAA Tournament regardless of its performance this week.
The Eagles advanced to the conference tournament semifinals for the first time since 1997, when they won four games in as many days to capture the title.
Marquette nearly did not make it past the quarters this time. An 18-point, first half lead was sliced to two twice in the second half.
"We gave them everything we had," Pitino said. "It wasn't enough and that's a tribute to Marquette."
Capitalizing on a pressing defense, Luke Whitehead brought Louisville within two points both times, hitting a layup with 6:03 to play and a dunk with 5:21 left to cut the Cardinals' deficit to 67-65.
"We should have done more of what coach told us and that's press," Whitehead said. "By pressing, we forced them to play our style of play and we were able to get back in the game."
Wade and Henry combined for 10 points during an 11-4 run that gave Marquette a 78-69 lead with 44 seconds remaining.
With Louisville unable to convert in key situations, Wade scored six straight points for the Eagles during the spurt, including a driving dunk with 4:26 to go.
The 5-10 Henry went nine of 18 from the field as Marquette made 47 percent of its shots.
Houston, the sixth seed, got a 26-point performance from Marcus Oliver to upset the third-seeded Tigers. Anthony Rice led Memphis with 15. Charlotte advanced past Tulane thanks chiefly to Jobey Thomas' 22 points.