Indeed Pivac's side had it all to do as Connacht took a seven-point lead into half-time, but tries after the break from Steffan Evans and Michael Collins paved the way for a nail-biting 21-19 finish.
The GUINNESS PRO12 will now be put to bed for a fortnight as teams return to European action.
And though Pivac admits the result is the type of confidence boost that could set his team up for the rest of the season, he is wary of letting it go to waste.
"We knew it was going to be another close game, staying in the game for the full 80 and working hard for each other was discussed at half time," he said.
"I was happy with the urgency and intensity that we came out with for the start of the second half; it was certainly the reaction we were looking for, although our team management allowed Connacht to put their foot back in the door.
"Overall, we are happy to get away with the win as it's so tight towards the top of the GUINNESS PRO12 table.
"We are back on top for now, however we are taking nothing for granted; it was a massive game, it buys us another week and another boost of confidence that we will need to take into the tough run to the end of the season."
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Guinness PRO12 Scarlets News
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