Ed Daniel had 19 points and 11 rebounds while Donte Poole added 13 points for the Racers (16-0, 4-0 OVC), who shot 54.5 percent in the game.
Josh Terry had 16 points, Melvin Baker added 14 points and seven boards while Jerome Clyburn added 11 points for the Governors (3-13, 0-3), who have dropped their past four.
"The best thing was, we played hard," said Austin Peay head coach Dave Loos. "We got behind and we were able to play hard, fight back and get back into it. On the flip side, we've got some guys that are too impatient. They wanted to come down and shoot it on one or two passes."
Holding a two-point lead, Murray State got consecutive three-pointers from Canaan to spark a 10-0 run for an 18-6 lead.
Another 9-0 run later in the first half made it a 32-15 game with nine minutes to play after a Zay Jackson jumper.
Austin Peay got eight straight points late in the first half to cut its deficit to 45-40 after 20 minutes of play.
The Governors kept it close in the early part of the second half, but were never able to take the lead or get closer than four.
Poole scored eight straight points, with the last six coming on back-to-back three-balls for a 57-45 lead with 15 minutes to play.
Austin Peay just wouldn't go away and made it a two-point game at one point and trailed by five with just over a minute to play, but Murray State hit its free throws down the stretch.
Murray State hosts Jacksonville on Thursday...Austin Peay hosts Eastern Kentucky on Thursday...Murray State has won four of the last five against Austin Peay and leads the series, 71-41...The 16-0 start ties the best in Murray State history, set during the 1935-36 season. The all-time win streak at MSU is 17 set by the 31-5 team from 2009-10.