Defender Frazer Wright stabbed the Perth outfit ahead after just 19 minutes from David Wootherspoon's corner to give them a crucial away goal in Trondheim.
But the win was only secured after Northern Irish stopper Mannus pulled off a string of important saves in the 20 minutes following the half-time interval.
Boss Wright - who has worked with Mannus as the Northern Ireland goalkeeping coach - said he was "proud" of his men but reserved special mention for his compatriot between the sticks.
He told BBC Radio Scotland: "I have known Allan a long time and I have never, ever doubted his ability. He knows that.
"I said before the game 'you have been here before with Shamrock Rovers. I know I can depend on you tonight'.
"'I know when called upon you will make the saves that you'll do and I know that you're experience will get us through the game.'
"I was pleased for them all. It's easy to pick out the goalkeeper but there were lots of headers and blocks at the end - stuff that we love doing."
Goalscorer Frazer Wright is now hoping that the Scottish Premier League outfit can complete the job and see off the former Champions League quarter-finalists in the return at McDiarmid Park next Thursday.
He said: "It gives us a great chance, we just need to go in with the same attitude as we did today, get the clean sheet and hopefully we will be through."
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