Sean Maitland went over for Glasgow's second try

Warriors ran in five tries as they outgunned their highly-fancied opponents, who have made a strong start to their domestic campaign in the Aviva Premiership .

Centre Mark Bennett grabbed a brace, while further scores from Sean Maitland, Tommy Seymour and replacement Niko Matawalu ensured the bonus point victory. Fly-half Duncan Weir contributed 12 points with the boot.

The Warriors headed into the European Champions Cup on the back of a strong run of form at the start of the PRO12 season, while Bath were looking to bounce back from a narrow defeat to Wasps a week earlier.

And it was two tries in the final quarter of the game that finally killed off the English side's hopes of an away win, following an intriguing arm wrestle in the first half.

Bath made the strongest start to the game and were three points in front through George Ford's fifth-minute penalty.

Mark Bennett crashed over for the Warriors shortly after to put the host in front, with Duncan Weir adding the conversion, but Bath quickly restored their lead.

Jonathan Joseph hacked the ball forward following a Glasgow mistake before pouncing to score, and Ford was again on target.

But that was it as good for the English side, as indiscipline cost them their lead before half-time. Weir struck two penalty goals to put Glasgow in front, before tries from Sean Maitland and Tommy Seymour made it 23-10 at the interval.

And the Warriors defence held firm for the minutes that followed the interval, before they laid their own platform and killed the contest in the final quarter.

Nikola Matawalu scored a great kick and chase try, converted by Weir, before Bennett broke and put boot to ball to score another well-crafted Glasgow try. Weir added the extras to make it 37-10 and there was no way back for Bath.

Glasgow head coach Gregor Townsend: "We are delighted with the performance from the team, the intent we played with and our defence, having not conceded a try after the 11th minute.

"It is the best team performance we have had this season.

"There was a period in the middle of the second half where we kicked away possession, maybe subconsciously thinking that we could defend the lead, but after that we attacked again, which was great to see. It was a really good 80-minute performance."