Sam Pinder went over for a try after less than two minutes to give Glasgow a great start but Celtic Warriors came back to avenge their Celtic Cup first-round defeat in September. Both sides scored two tries each but 19 points from the boot of Neil Jenkins saw the Welshmen through.
Other Glasgow scores came from a try by Alan Bulloch, Calvin Howarth had a penalty as well as converting Pinders try and Dan Parks converted the Bulloch try and kicked an injury-time penalty goal that secured Glasgow's first bonus point of the competition. Glasgow's other three points came from a drop goal by lock Andy Hall.
Next week's Celtic Cup match with Ulster may be a daunting prospect for Glasgow but it provides a welcome diversion from a disappointing Celtic League campaign that sees them bottom of the heap after eight games.