Dan Evans scored a game-high 17 points to pace Lawrence, ranked 10th by D3hoops.com. Jim Capelle led the 17th-ranked Titans with 14 points.
Lawrence (4-1) matched its biggest lead of the game at 31-22 before the game tightened. Oshkosh (7-2) cut the lead to 31-30 but couldn't get over the hump.
The Titans stayed close and trimmed the Lawrence lead to 46-44 with 59 seconds left. Evans answered for Lawrence, as his high-arcing layup over 7-foot-1 center Kerry Gibson gave the Vikings a 48-44 lead with 24 seconds left.
Brendan Falls and Chris Braier both hit a pair of free throws in the final 10 seconds to seal the victory for Lawrence.
Braier finished with nine points and a game-high 11 rebounds. Kyle MacGillis added nine points for hte Vikings. Lawrence held Gibson to eight points and seven rebounds, and Oshkosh's leading scorer, Andy Jahnke, was limited to four points and one rebound.
Coupled with Lawrence's win earlier this season at UW-Platteville, this marked the first time the Vikings had beaten WIAC teams in consecutive games during John Tharp's tenure as head coach. Oshkosh is now 75-7 in its last 82 nonconference games, and two of those losses have come to Lawrence.