Braier became the 17th player in Lawrence basketball history score 1,000 points. He stood at 971 entering play on Saturday and scored 36 points to go along with his 13 rebounds. Braier hit 15 of 18 shots from the floor in 37 minutes.
Lawrence (13-3, 8-2 MWC), ranked 12th in this week's D3hoops.com Top 25, got 35 points from Jason Holinbeck. Kyle MacGillis added 17 points for the Vikings.
Eric Walsh paced Grinnell (4-13, 1-9) with 13 points.
Lawrence carved out a 45-37 lead at the half, but started the second half with a 9-2 run to grab a 54-39 lead. Grinnell did cut the lead to 61-53 with 13:53 left in the game, but the Pioneers never got closer than that.
Lawrence built its lead to as many as 18 points and cruised to the win.
The Vikings shot 62.9 percent (39-62) from the floor and piled up 25 assists on their 39 baskets. Brendan Falls had a game-high seven assists and MacGillis added six.
As is normal against Grinnell, the Vikings enjoyed a huge advantage from the foul line. Lawrence was 22 of 32 from the line, and Grinnell, which didn't shoot a free throw until the second half, was 6 of 7.
Lawrence has now won three straight against Grinnell.