With the win, the Huskies (5-3) finish third in the Canada West division and will face provincial rivals the Regina Rams (6-2) in a semifinal on Nov. 2 at Mosaic Stadium.
The No. 7 Rams blanked the University of Alberta 19-0 in Friday's other CIS game.
The Thunderbirds wrapped their season with a 2-6 record.
Saskatchewan's Cole Samson and UBC's Thomas Moult traded field goals early in the first quarter before Burko hit Charlie Power with a 34-yard TD pass at 1:40 to go ahead 10-3.
Burko carried the momentum into the second, finding Mitch Stevens with a 52-yard touchdown pass to make it 17-3.
Shane Buchanan punched in a touchdown from the one-yard line two minutes later for the Huskies, but UBC cut into the lead with a 15-yard touchdown reception from Patrick Bull at 6:24 to cut the deficit to 24-10.
Saskatchewan entered the half up 31-10 after Chase Bradshaw ran in a major from the red zone with 1:47 left in the second.
Burko hit Stevens again from 35 yards out for the only score of the third.
Daniel English opened the fourth with a 12-yard touchdown catch for the Thunderbirds, but Jarvis James put Saskatchewan up 45-17 when he ran in a TD from 68 yards out.
Burko found Braeden George from eight yards out and UBC's Lucas Spagnuolo run in a TD to round out the scoring.
No. 7 Rams 19 Golden Bears 0
At Regina, Landon Buch's touchdown rush from the one-yard line in the second quarter was all the offence the Rams needed to keep the University of Alberta (0-8) winless on the season.