This extraordinary 10-3 aggregate win in remote southern Russia - just 40 miles from the border with the war-torn Chechen Republic - took Rangers through to the group stages for the third time in five years.
McCoist struck after only 33 seconds and then again in the 13th and 18th minutes to become the first Ibrox player to score a hat-trick in Europe for 10 years. His second hat-trick in five days raised his goal record in Europe for Rangers to 16.
Stuart McCall and Laudrup were involved in his first as they set up Alex Cleland to cross from the right and McCoist planted a header beyond the despairing goalkeeper, Zaur Khapov from, 10 yards. His second goal was another header, this time from a cross by Jorg Albertz.
Rangers were caught out within 60 seconds as Igor Yanovski thumped home from the edge of the box. McCoist soon replied, though, as Sergei Timoteyev conceded possession to Van Vossen and he presented McCoist with a simple chance to complete his hat-trick.
In the 24th minute Rangers were pegged back once again as Nazim Suleimanov converted from the penalty spot after Albertz had pulled down Zaza Revishvili. Ten minutes later the Rangers captain, Richard Gough, was booked for a foul on Omari Tetradze, but five minutes from half-time the Scottish champions grabbed a fourth goal, Van Vossen rounding the goalkeeper from a McCall pass to fire home.
Before the interval Rangers had to take the defender Gordan Petric to the sidelines for treatment as blood streamed from a head cut, but he returned wearing a bandage. Ten minutes after half-time, Rangers went 5-2 up as Laudrup streaked away on to a Van Vossen pass to round the goalkeeper and find the net.
After McCoist had been taken off in the 75th minute, with Gordon Durie coming on, Laudrup added his second and a sixth for Rangers with seven minutes left. He blasted home after McCall had set him up when Durie's shot had struck a post. Rangers completed an incredible aggregate win when another substitute, Miller, tapped home from Laudrup's pass with four minutes left.
Alania Vladikavkaz: Khapov; Revishvili, Timoteyev, Sheliya, Vzhioev, Tetradze, Tedeyev (Agaev 27), Yanovski, Kornienko (Skish, 78), Kanishev, Suleimanov, Agaev (Derkavh, 57).
Rangers: Goram; Cleland, Albertz, Gough, Petric, Bjorklund, McCall, McInnes (Durrant, 84), McCoist (Durie, 75), Van Vossen (Miller, 67), Laudrup.
Referee: U Meier (Switzerland).Reuse content