They have a 100 per cent record at home but they have lost their last three matches in all competitions - twice to Clermont and once to Ulster last time out in the RaboDirect PRO12 - for the first time since May 2010.
Cullen and co will take heart from the fact that Connacht have won just once away to Irish opposition - at Leinster in 2002 - since the start of the competition but earlier this season they were 34-6 winners in the reverse fixture at the Sportsground.
But Cullen is only too aware that his side must improve quickly to get back to winning ways and mount an assault in the RaboDirect PRO12.
"From our perspective we have to try and build some momentum coming into a busy next few weeks which will go a long way to defining the rest of the season," said Cullen.
"This weekend Dan Parks will punish any penalties we give away because he has such a high kicking percentage and has proven himself time and again over the years.
"So we need to be more careful about giving quality sides easy opportunities to keep the scoreboard ticking over. These kinds of games are won and lost over the finest of margins.
"So as 2012 draws to a close and we move into a new year, it's still all to play for. My first wish is that we get a few more points on the board. When we get a few more bodies on the deck that will boost competition for places because we've been disrupted through the first half of the season and we have lacked a bit of fluency thus far.
"By the end of January we'll know our fate and we have a bit of ground to catch up on. And, for us, that process starts this weekend."
Shane Jennings leads a young team with Heinke van der Merwe named in the front row alongside Aaron Dundon and Ireland prop Michael Bent, with Devin Toner partnering Ben Marshall in the second row.
Fergus McFadden starts on the right wing in a back three alongside Fionn Carr and full-back Andrew Conway while Ian Madigan joins Isaac Boss at half-back.
For Connacht, Eric Elwood makes four changes to the side that lost to Munster last time out as they look to improve on a run of one win in their last six RaboDirect PRO12 matches.
Matt Healy earn his first start and cap for the province while Danie Poolman moves to the right wing and makes way for Eoin Griffin who resumes his centre partnership with Dave McSharry.
In the pack, Denis Buckley is named in the front row alongside Jason Harris-Wright and Nathan White, the former Leinster prop captains the side tomorrow. Michael Swift, who returned from injury last week and came off the bench against Munster, will partner George Naoupu in the second row.
Elwood told the Galway Advertiser: "We are under no illusion we have another big challenge on Saturday. We had a good win against them earlier in the year and we are expecting a backlash up there.
"They are after losing the last couple of games so it's another difficult outing - nothing new there.
"The lesson [from the Munster game] is you have to able to take your chances. In tight ball games, decisions go for you or against you, but when you get opportunities to score, you have to take them."
At RDS Dublin, 7.45pm.
Referee: John Lacey (IRFU, 22nd competition game)
Assistant Referees: Leo Colgan, Mark Patton (both IRFU)
Citing Commissioner: Dennis Templeton (IRFU)
TMO: Jude Quinn (IRFU)
Live on TG4