The massive win moves the South African outfit up to fourth in the URC standings, four points behind Leinster with three rounds remaining.
Centre Henco van Wyk scored an early brace of tries while Erich Cronje dooted down in the corner as the Lions took a commanding 19-0 lead.
Flyhalf Dan Lancaster hit back for the Scottish side with a converted try but the Lions went into the halftime break 26-7 ahead with prop Asenathi Ntlabakanye securing the four-try bonus-point.
The hosts continue to dominate the early stages of the second half with flank Ruan Venter powering over for a try and Chris Smith adding the conversion.
Glasgow tried to fight back through captain Stafford McDowall but Lions scrumhalf Morne van den Berg scored under the posts to out the result beyond doubt.
Flank Siba Mahashe crossed for the seventh try while fullback Quan Horn put the seal on a dominant display for the Lions.
Sharks head coach JP Pietersen expressed deep frustration and concern after Springbok utility back Ethan Hooker suffered a serious shoulder injury in the Sharks' 21-17 defeat to the Ospreys in Swansea.
Lions coach Ivan van Rooyen hailed his charges' defensive effort in their 54-12 hammering of the Glasgow Warriors in the United Rugby Championship on Saturday.
Stormers Director of Rugby John Dobson was an unhappy man following his charges' 24-33 loss at the hands of a rampant Connacht side in the United Rugby Championship on Saturday.
The Sharks slumped to a 21-17 loss at the hands of the Ospreys in their United Rugby Championship clash on Saturday night at Bridgend in Wales.
