A similar objective will inform the Warriors' bid to achieve a positive result this weekend, with their recent good tournament form positioning the Scotstoun-based club in third place going into the Round 15 games.
As an indicator of how tough a battle awaits them, Glasgow need only recall the 37-8 defeat they suffered in the same fixture on the very same date last year. They haven't beaten Connacht at any venue since October 2009.
Head coach Lineen told www.glasgowwarriors.org: "The defeat in Connacht last season was our worst performance and result of the campaign, and everyone involved this weekend is desperate to avoid coming away feeling as bad as we did that day.
"We've racked up a few good results in the RaboDirect PRO12, and were pleased with the way the team performed in beating Scarlets at Firhill, but we're at a stage of the campaign where every performance has to be absolutely spot on.
"That's doubly the case at a tough away venue like Connacht, where you've got a passionate home team and crowd against you. We've not done well in Galway of late, and that's something we need to put right to ensure we stay in the right area of the RaboDirect PRO12 table."
Encouraged by the team's display in seeing off the men from Llanelli, Lineen has kept personnel changes to a minimum for the visit to the Sportsground.
The one switch in the starting line-up sees Pat MacArthur replace Dougie Hall at hooker.
Among the replacements will be the RaboDirect PRO12's leading points scorer Duncan Weir, who was an unused substitute for Scotland in their RBS 6 Nations match against Wales last Sunday. The side will be captained by Graeme Morrison, who now sits second in the list of most individual minutes completed by any player in the competition. Al Kellock is in fourth place.
Lineen continued: "The guys who played against Scarlets have more than earned the right to try to claim us another win on Saturday.
"In terms of the change in the front row, we've got four hookers [MacArthur, Hall, Fergus Thomson and Finlay Gillies] who are all more than capable of filling the jersey, and we want to give them all a window to impress. Dougie and Fergus were our two for Scarlets, and now Pat and Finlay have the chance to do the business this weekend.
"Every game is massive for us at this point in the season, and we're confident the players will be inspired by that level of pressure and opportunity."
GLASGOW WARRIORS TEAM TO PLAY CONNACHT IN THE RABODIRECT PRO12 AT THE SPORTSGROUND ON SATURDAY 18 FEBRUARY (KICK-OFF 5.30PM, LIVE ON BBC ALBA)
15 Peter Murchie
14 Tommy Seymour
13 Troy Nathan
12 Graeme Morrison (Captain)
11 David Lemi
10 Ruaridh Jackson
9 Henry Pyrgos
1 Ryan Grant
2 Pat MacArthur
3 Jon Welsh
4 Rob Verbakel
5 Tom Ryder
6 Rob Harley
7 Chris Fusaro
8 Ryan Wilson
SUBSTITUTES
16 Finlay Gillies
17 Gordon Reid
18 George Hunter
19 Nick Campbell
20 Duncan Weir
21 Alex Dunbar
22 Colin Shaw
23 Calum Forrester
Not considered for selection due to injury: Johnnie Beattie (elbow), Mike Cusack (ankle), Rob Dewey (shoulder), Ed Kalman (neck), Moray Low (knee), DTV van der Merwe (shoulder).