The Icelandic midfielder made his first start for the Toffees since making a £45m switch from Swansea earlier this month – and needed just 45 minutes to show it was money well spent.
Having conceded a goal shortly before half-time – another screamer, this time from Split midfielder Josip Radosevic – Everton came out of the traps in the second half knowing another goal from the Croatians would send the tie to extra-time.
But Sigurdsson turned the game on its head barely 15 seconds after the restart, hounding a Split defender in possession before intercepting a pass.
The rebound fell to him on the half-volley more than 50 yards from goal but he unleashed an audacious dipping volley that flew over the stranded goalkeepers head and into the net.
Twitter lit up in amazement after the wonderstrike, with fans piling in to lavish praise on the 27-year-old.
“The presence of mind to even attempt that, my goodness,” gushed one supporter.
“He must've seen the keeper off his line all game and thought to himself ‘the next ball that pops up in front of me is going towards goal’.”
Another wrote: “Probably one of the best goals I'll see this year.”
“My god what's up with these goals,” a third chipped in.
“This match is crazy.”
It comes amid reports that travelling Toffees fans had been attacked by hooligans in the Croatian city in scenes similar to those seen at Goodison Park last week.
One man was reportedly hospitalised with a head injury but his condition is not thought to be serious.
Everton will face Lyon, Atalanta and Apollon Limassol in the Europa League group stage after the draw was made today (August 25).
