Rangers started the Uefa Cup group phase with a comfortable win in Poland.
Peter Lovenkrands shot the Ibrox side into an early lead and substitute Nacho Novo stroked in another goal 10 minutes after the break.
A poor home side seldom threatened keeper Stefan Klos and Fernando Ricksen shot home a third from 20 yards.
Shota Arveladze added a penalty after he had been tripped and Steven Thompson headed in a simple late goal as Amica Wronki folded in the closing stages.
There was a let-off for Rangers in only the second minute when Pawel Kryszalowicz was able to slip free on the right and set up Marteusz Bartczak in the area.
The midfielder's first touch was good to tee up the shooting chance but with all the goal to aim at he fired wide of Klos' left-hand post.
In the 17th minute Lovenkrands fired Rangers ahead with a smartly-struck shot from just inside the left of the area.
Arveladze was the man who made it by nipping past two challengers to reach the penalty box and when Lovenkrands found the ball at his feet he had the time and space to lash a low shot home.
As a dull first half drew to a close, Jacek Dembinski crossed from the right and picked out Kryszalowicz in the box but, although the striker's header was accurate, it did not have the pace to trouble Klos.
The second half started brightly and Dado Prso headed home a Gregory Vignal cross but the flag was up for offside to rule it out.
The Croatian was back in a scoring position within seconds but fired across goal and inches wide under pressure.
In the 54th minute Rangers swapped Lovenkrands for Novo and he made an instant impact with the second goal two minutes later.
Vignal's cross from the left was back-heeled by Prso into the Spaniard's path and his shot from the edge of the box beat the goalkeeper.
Luck was with Rangers when Krysalowicz headed on a Burkhardt corner for Dembinski to smash a first-time effort back off the crossbar.
And Ricksen killed off the home team in the 69th minute by drilling home a 20-yarder after Prso had laid the ball back to him.
Arveladze was fouled just inside the penalty area and he picked himself up to slot home the fourth from the spot in the 73rd minute.
Substitute Thompson looked hungry for a goal and was helped out by keeper Malarz, who punched Burke's delivery straight to him, and he headed the ball into an empty net from 12 yards.
Amica Wronki: Malarz, Bieniuk, Dudka, Kucharski (Sobocinski 46), Skrzypek, Stasiak, Dembinski, Gregorek (Kikut 59), Kryszalowicz, Bartczak, Marcin Burkhardt (Kowalczyk 67).
Subs Not Used: Mielcarz, Dziewicki, Wojtkowiak, Filip Burkhardt.
Rangers: Klos, Khizanishvili, Andrews, Boumsong, Vignal, Ricksen, Malcolm, Arveladze (Namouchi 79), Lovenkrands (Novo 55), Prso (Thompson 71), Burke.
Subs Not Used: Graeme Smith, Hughes, Ball, McLean.
Goals: Lovenkrands 17, Novo 57, Ricksen 69, Arveladze 73 pen, Thompson 89.
Ref: Julian Rodriguez Santiago (Spain).