Matt Williams' side are now eight points clear of bottom side Connacht with just two rounds of matches remaining and are in touching distance of that third Irish qualifying spot in the Heineken Cup.
The games are coming thick and fast for Ulster towards the tail end of the season. Saturday's encounter with Glasgow is their second of three fixtures in a ten-day period.
Flanker Matt McCullough, who has played in all seven of Williams' games in charge of Ulster to date, is keen for the province to chalk up their sixth straight win at Ravenhill this weekend as a thank you to both the players moving on and their loyal supporters.
McCullough said: "There is a really quick turnaround to Glasgow on Saturday so we spent Thursday morning in recovery, working with our fitness coach Phil (Morrow) and GG (physio Gareth Robinson) on any problem areas.
"We will have a light Captain's Run on Friday and then play the match on Saturday.
"Glasgow are a good solid side and have done extremely well this season. We are coming to the end of a really hard season, but, on Saturday it is about Ulster playing at Ravenhill.
"We need a good performance to propel us forward in the league to ensure Heineken Cup rugby for next season," he added.
"Also, for the players who are heading off to pastures new, we want to send them off in a positive frame of mind. Finally, we want and need to thank our supporters for sticking with us this season."
Reflecting on Ulster's hard fought 19-9 win over Munster, McCullough paid tribute to the fans - most of the 12,300-strong crowd - that roared the hosts on during Wednesday's interprovincial clash.
"It was a tough night and a tough ask. Munster are always a hard side to beat so we were pleased to have come through with three tries. It was a good start for the first of three really important games in 10 days.
"It was tough out there when Munster got on top but the support of the fans really helped us through. I thought Wednesday was the loudest we have heard the crowd all season and there was such a buzz around the ground."
Ulster's winning form at their Belfast base has been crucial in keeping them in the running to make next season's Heineken Cup and two Ulster and Ireland legends have had an input off the pitch.
"Mike Gibson and Paddy Johns have both spoken to us this season about how mentally Ravenhill is our home and how we have to defend the try line like we are defending our home," McCullough revealed.
"It made such a difference to us on Wednesday night when we were defending our line to hear the roar from the crowd. When we were driving Munster back and the crowd started chanting 'Ulster, Ulster, Ulster' - it lifted us and we spoke about it afterwards how it made the difference."