The home side had to come from behind to overcome the Blues 29-13 to secure their seventt win in a row and fifth successive five-pointer to claim a new league record surpassing the one set by the Dragons in 2004.
With a superior points difference to Ulster, Glasgow find themselves at the top of the table on 61points.
Phil Davies’ side had jumped out to a 13-10 lead after flanker Josh Navidi, released by the Welsh camp, crossed to score with fly half Rhys Patchell adding the conversion along with two penalties.
Peter Horne had earlier danced through the Blues midfield to score in the 17th minute with Duncan Weir converting while the Scottish pivot closed the gap further with another penalty before the break.
Glasgow began the second half by driving a lineout deep into the visitors’ half but repeatedly lost possession so could not capitalise.
Matawalu had moved from scrum-half to right wing and he scored the vital try after getting to his own long kick first, with Weir adding the extras.
Glasgow secured the bonus points with two more tries in the next nine minutes through Weir and Manawalu.
