With only three away league games remaining for Scarlets this year, they will enter 2015 having secured ten wins and one draw in the previous 12 months.
A low-scoring first half under the Friday night lights at Parc y Scarlets saw the home side go into the break with a 9-3 lead.
Glasgow fly-half Peter Horne's two penalties levelled things up before Scarlets kicker Steven Shingler put his side back in front with 64 minutes played.
A tense final quarter of the game ensued but replacement Rory Pitman barrelled his way over with three minutes to go to secure a 19-9 victory.
The win means Scarlets climb to sixth in the GUINNESS PRO12 table, just five points behind their opponents who lie fourth.
And while Pivac believes the West Wales region should have wrapped the game up earlier, he pinpointed his forwards, which included man-of-the-match James Davies, as the difference makers.
"We probably blew a couple of opportunities which put a bit of pressure on ourselves," Pivac told the South Wales Evening Post.
"But I am happy to get the four points and to not concede a bonus point to Glasgow was also important.
"I thought our set-piece was good - our scrum and line-out went well. It is an area we are going to really focus on in this next block with the weather coming in.
"There are going to be a lot more set pieces in the game and a lot tighter play, if you like. We have ground out two wins in the wet in the last two rounds.
"I guess we have kept that dream of being in the mix at the end of the season alive. If we hadn't won tonight we would have been up against it."
View the best images from Scarlets' Friday night victory over Glasgow Warriors by clicking here.
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