Manager Derek McInnes says Tromso "thought they had one foot in the next round" before Joe Wright's first-half header sent Kilmarnock into the Europa Conference League play-offs.
After a 2-2 draw in the first leg at Rugby Park last week, McInnes' side headed to northern Norway as underdogs.
But, aided by a deceptive deflection that scuppered goalkeeper Jakob Haugaard, Wright's 11th-minute goal proved decisive to send the Scottish side through.
The 300-strong travelling support watched on as a robust defensive display ensured Kilmarnock advance to face FC Copenhagen, who beat Czechs Banik Ostrava on penalties, for a place in the league stage.
"I thought there was an overconfidence [from Tromso], we spoke about that," McInnes told BBC Scotland.
"We played on the outside of their shape really well in the first half, but behind that there was a real solid shape and we got the all important goal.
"We wanted to try to continue this run in Europe and we've now got a really exciting tie to come."
Unsurprisingly, it was Danny Armstrong who provided the assist for Killie's opener. The winger's corner found Wright, whose header clipped off an unsuspecting Vetle Skjaervik's shoulder and into the roof of the net.
Tromso threatened after going behind, with midfielder Kent-Are Antonsen pulling the strings. His crosses continually caused chaos, with Liam Donnelly and Bobby Wales both called upon to hook clear goal-bound efforts.
A moment of uncertainty came for the visitors when goalkeeper Robby McCrorie was judged to have picked up the ball after already handling it. An indirect free-kick was awarded, but Tromso failed to capitalise.
The visitors had dropped deep immediately after the opener and successfully stuck with that defensive shape for the majority of the 80 minutes that followed.
Not long after the offside flag prevented a Leo Cornic equaliser for the hosts, centre-back Amadou Barry should have levelled when his header crashed off the woodwork from just two yards out.
A late onslaught from Tromso set up a nervy end to the increasingly feisty encounter, but a resilient defensive effort kept out the hosts as they threw every body forward in the last moments to no avail.
Killie's hardiness ideal for continental football
Kilmarnock’s grit in defence has shone once again.
As soon as McInnes’ men took the lead in the Arctic Circle, there was a noticeable lowering of their defensive line as 11 bodies quickly dropped behind the ball for Tromso’s next attack.
Club captain Kyle Vassell and young, surprise starter Bobby Wales both fluffed chances up the other end in the second half, but it never seemed to unsettle Killie.
Every player held their shape well and rarely allowed Tromso a clear sight at goal, while also effectively slowing down play in the latter stages of the tie.
The late introduction of Rory McKenzie was also inspired, as a late last-ditch challenge from the midfielder thwarted a promising Tromso attack.
The Ayrshire side are now within touching distance of the league stage - and it is down to their battling attitude and tactical nous when out of possession.
What the manager said
Kilmarnock manager Derek McInnes: "Last season, we had so many games where we got results from being resilient, hard to play against, strong defensively, everything we weren't on Sunday.
"There was an acceptance from us that we had to defend better and we had to be more confident in our defending. We reminded them of how good we have been.
"[Wright] was in such a poor place on Sunday. He felt like he let everyone down, but in football there's always another game. He's the guy who made the difference tonight."