The European minnows ended a 21-match winless streak, and won a non-friendly international for the first time since 2011 as they edged the Moldovans 1-0 in Chisinau.
The visitors struck in the 74th minute through Franz Burgmeier, as they won a competitive away match for the first time since beating Luxembourg in World Cup qualifying in 2004.
Pauritsch insisted the occasion will not be lost on the team, as they put three points between themselves and the side they conquered at the foot of Group G.
"We are happy about everything. This is our tenth victory. We have won for the first time in two years," Pauritsch said.
"It's absolutely brilliant that we won an away game. We have the opportunity to have a great celebration. Don't worry, we shall do it.
"Our task in this group is to not finish bottom. We claimed a victory tonight and we want to take points in our next games.
"We play defensive football. From time to time it produces good results for us. Tonight is a holiday for us."
Moldova coach Alexandr Kurteyan was already plotting retribution, however, as he felt Liechtenstein were fortunate to claim all three points.
"I am sad about the result. But I am even more sad about the quality of the game – I expected the opposite," Kurteyan said.
"Liechtenstein were lucky tonight but after the away game we shall be the winners.
"You need to score to win. We created enough good chances but most of our shots were off target.
"We work a lot on set pieces but this evening could not do anything with them."