Midfielder Barry Bannan said Gibraltar's goal "shook Scotland into life" before his side eventually ran out 6-1 winners at Hampden.
Shaun Maloney's penalty was cancelled out by Lee Casciaro's strike - Gibraltar's first competitive goal.
But Maloney added another penalty and Steven Fletcher grabbed a hat-trick, with Steven Naismith also scoring.
"We've came out the other end winning the game like we should have," Bannan told BBC Scotland.
"You just want to win the game comprehensively and I think after they scored that shook us into life a little bit."
Scotland lined up with an unfamiliar three-man defence and initially struggled to control the game.
"It's completely different to what we're used to," said Bannan of his team's approach in Sunday's Euro 2016 qualifier. "They came here to frustrate us and it's a bit of a shock as we're not used to that.
"It probably took time to get used to the formation and get used to the way they were setting up.
"In the end, when we figured out how to get in behind and how to hurt them, we did well and it could have been more.
"In this group so far, when the games have been close, it's counter attacking we're a lot better at.
"But this was a different task, it took us a while but we came out the other end perfectly."
Scotland, third in Group D with five points from 10 games, play the Republic of Ireland in June. A win in Dublin would put Scotland a commanding five points clear of Martin O'Neill's side, who sit fourth after their 1-1 draw with Poland.
"It's a massive game," said Bannan, who is on loan to Bolton Wanderers from Crystal Palace.
"This was just all about getting the three points and getting a couple of goals as well.
"We're just looking forward to this Ireland game now. It's going to be a massive game. We know in that dressing-room we've got enough to go over there and win."
Bannan was also delighted to see Fletcher hit Scotland's first hat-trick since Colin Stein in 1969 - also his first goals for his country since 2009.
"He's a top striker and top strikers when they're confident are very hard to handle," he said.
"It was brilliant for him to get a hat-trick and hopefully that kicks him on now and he can score many more in the future."