Everton had fallen behind two minutes before the interval to see their two-goal first-leg advantage over the Croatian team sliced in half, when Sigurdsson took matters into his own hands.
The second half was only 13 seconds old when the Club’s record signing pounced on a defensive slip to volley home a stunning 40-yard goal.
That left Hajduk needing a further three goals to prevent Ronald Koeman’s men from safely negotiating this Europa League play-off round tie – a task that was beyond the hosts despite the clamorous backing of their fervent support.
“Personally, it was fantastic to get my first goal for the Club – and in a fantastic stadium and fantastic atmosphere as well,” Sigurdsson told evertontv.
“I probably did not expect to score from there. But I managed to get a touch on the ball – it was sitting up quite nicely and I thought to myself, ‘the keeper is probably not on his line’… so I decided to go for it and, thankfully, it beat the keeper and hit the target.
“We are going home happy, which is the main thing. The most important thing was to get the result and be in the hat for the draw.”
Sigurdsson insisted his focus before kick-off had primarily been on getting through the match, given he had played only 29 minutes this season – as a substitute in Everton’s Premier League draw at Manchester City on Monday.
The 27-year-old was delighted, therefore, to be on the pitch from the first whistle until the last – even if it needed a bit of kidology from Koeman to cajole him through it.
And after savouring the crackling atmosphere in Hajduk’s Stadion Poljud - and sampling his first taste of playing for the Blues’ wonderful travelling support - Sigurdsson was already looking forward to getting stuck into the Europa League’s group stage.
“I was just fully focused on how tough this game was going to be and making sure I got through it, fitness wise,” added Sigurdsson.
“It was my first start since pre-season and my first 90 minutes. I am a bit tired but I really enjoyed it. It was a good night for me personally and for the team.
“The manager kept saying to me, ‘10 more minutes, 10 more minutes’. He must have said it three or four times. Then I looked at the clock and it said 85 minutes. But at the end he said, ‘you needed the minutes’!
“But the last 10 minutes wasn’t too difficult, we were keeping the ball really well and making them chase it. It was pleasing for me to get through it, get 90 minutes under my belt and get the goal as well.
“It was a great night of football, the home and away fans were terrific. These are the kind of nights you want to be involved in, in big stadiums, with great fans.”