Scotland followed up the 34-24 bonus-point victory over Romania by winning an attritional World Cup Pool B battle against Georgia 15-6 at Rugby Park Stadium in Invercargill, with Parks kicking four penalties from seven attempts and a drop goal and Merab Kvirikashvili replying with two penalties.
With Scotland leading 9-3 as time expired at the end of the first half, Cardiff Blues fly-half Parks nearly undid all his good work.
His poor attempted clearance to touch was blocked and Georgia forged forward, but Scotland stopped them and Parks was reprieved.
Parks said: "It's one of those things that hasn't cost us, but it could've cost us.
"Andy certainly wasn't happy, but he's all right now, because we won.
"I thought Georgia had done a knock-on, because the ball did go forward.
"I was just going to kick the ball out. I was a bit casual, the ball came off the side of my foot, hit Nathan (Hines) and panic set in.
"But as it turned out I got onto the ball and held it up, Sean (Lamont) helped me out.
"It was hairy, but it was all good at the end."
It certainly was as Scotland extended their winning run to five ahead of the September 25 clash with Argentina in Wellington before the October 1 bout with England in Auckland.
Scotland travel to New Zealand's capital on Thursday where they will seek to maintain their record of progressing from the pool stage at every World Cup tournament.
Parks added: "We still have more to offer and we're looking forward to the big games coming up.
"We've done well in these two games, but we move forward and we're full of confidence."
The victory saw Rory Lawson extend his 100% record as captain and all but secured at least third place in the pool and qualification for the 2015 World Cup in England.
The Gloucester scrum-half paid tribute to the forwards.
Lawson said: "They were outstanding. The front five and the pack in general were immense.
"It was great to see that. There's been a lot said in the last few days.
"After the Romania game, talking about the Georgians, a lot was made of their strengths.
"But we went out today and our front five and pack put in an outstanding performance.
"They can really hold their heads high after that."
Tighthead prop Euan Murray was the foundation stone of Scotland's scrum and provided the forward impetus, but the Newcastle prop is unlikely to feature against the Pumas due to his refusal to play on Sundays for religious reasons.
Second rows Jim Hamilton and Nathan Hines thrived and the back row of Ross Rennie, Alasdair Strokosch and Kelly Brown were outstanding. Brown was awarded man of the match.
The Saracens ace, who played at number eight against Georgia having played flanker against Romania, said: "We expected a big physical test, we certainly got that.
"We knew we had to play a fairly strict game plan and a bit of territory and I felt we controlled it well.
"Our team and our forwards really imposed themselves.
"Our tight five boys did an absolutely fantastic job and it was a joy to be on the back of that."
Hamilton was key to the effort.
The Gloucester lock said: "It went well. I thought we had them up front for the majority of the game.
"We had to be on the ball. Our guys turned up from minute one in the scrum and maul.
"As a forward pack we're pretty happy."
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