The Warriors have never won more than six consecutive tournament matches, and after Saturday’s 24-13 victory away to Benetton Treviso.
The Dragons game is the first Warriors match this season not to be televised, so the only way to see the action live is in person at Scotstoun Stadium.
Head coach Gregor Townsend has made a rallying call to Glasgow supporters to continue the "fantastic backing" provided in the first four games at Scotstoun.
The head coach told glasgowwarriors.org: "The players and coaches have all been really impressed with the support we've received from the crowd so far this season.
"To sell out the Ulster game a fortnight ago, the first time we've done that for a match outside the derby against Edinburgh, was a tremendous effort from the fans, and we need them with us again this week.
"The players have done very well to put together some positive results in the RaboDirect PRO12, and we now have the opportunity to continue that run in back-to-back home games against Dragons and Leinster.
"It's vital that we maintain the momentum we've established, but we know that the Dragons game is another massive test.
"Matches between these teams have tended to be very tight and hard fought over the seasons, and it's in that sort of close contest where having a great home crowd at your back can really make a difference."
Main and North stand seats are now on sale online, and by calling 0844 800 3490 (Monday-Friday, 9.00am-5.00pm). Tickets are also available via these channels for the covered East Terrace that was put in place before the recent match against Ulster.
Standing tickets are also available in store at the Gordon Street and Sauchiehall Street branches of Greaves Sports, Glasgow's official retail partner. Please note than Main and North stand tickets are not on sale at Greaves Sports.
Book in advance for a better choice of seats and to save £5 on match-day adult, student and senior citizen prices.