Scotland boss Gordon Strachan said he always felt his side would score a winning goal against 10-man Slovakia.
A late own goal from Martin Skrtel gave the Scots a narrow but important 1-0 victory at Hampden as they continue their late surge towards the play-offs.
It leaves Scotland needing to win in Slovenia on Sunday to ensure second place and a probable play-off place.
“At no time did it feel stressful. I could see they had everything under control,” said Strachan.
“It wasn’t a problem – apart from a couple of misplaced passes. They had a real belief in what they were trying to do and stayed above the anxiety of the crowd – a lot of people were getting anxious.”
While a draw would not have ended Scotland’s hopes, the fact Slovakia finish their campaign against Malta – who have taken just a point from nine matches – meant they would have been all but out.
Strachan sent on three second-half substitutes in search of the decisive goal at Hampden – and two of them combined for the 88th-minute goal.
Ikechi Anya’s cross was turned in by Slovakia captain Skrtel, under pressure from Scotland striker Chris Martin.
Slovakia had been playing with 10 men since the 23rd minute, when Robert Mak was shown his second yellow card, for a dive in the penalty area.
“I genuinely felt we would score, no matter what the time was,” Strachan said.
“There’s plenty of times I’ve felt like that and the goal hasn’t come, but I did feel it would with the work they put in, the way they tried to play.”
Scotland have now gone five games unbeaten in Group F, with only a last-minute goal from England’s Harry Kane depriving them of maximum points in that run.
They travel to Slovenia knowing a win would secure second place, though their hosts have yet to concede at home during the qualifying campaign.
“Slovenia was good, stuff against England was good, Lithuania was exceptional, Malta was workmanlike. So we’ve been building up to that performance,” Strachan said.
“And the players deserve a result like that. Many times we’ve been sitting here with bad luck written all over it.”
Slovakia goalkeeper Martin Dubravka did his best to keep Scotland out, pulling off four top-class saves, while Martin and Leigh Griffiths hit the woodwork before the breakthrough.
“The goalkeeper was outstanding,” said Strachan, adding: “The crossbar wasn’t too bad either!
“There was a lot going on we can be pleased with. Now we can regroup and go again.”
Strachan acknowledged he would have accepted sitting in second position after a slow start to the group.
“What we want to do now is try to finish this off and forget about bits and bobs that went on before,” he said.
Slovakia, who are two points behind Scotland, could yet claim second place, but coach Jan Kozak appears resigned to missing out on qualification.
“We are sad that two years’ efforts are in vain,” he said. “I don’t like to be in this position – relying on someone else’s help.
“We were unlucky as it looked like we were going to make it.
“We managed to keep possession, but it cost a lot of effort and we were very tired towards the end of the game.”
Kozac also hinted he had a theory about how events had conspired against his side, although he would not expand on the specifics other than their baggage being misplaced on their arrival.
“That’s how it started,” he said.
“Since our arrival in Scotland, there have been too many coincidences and I’m too old to believe in coincidences.”