Shelley Kerr’s team got off to a good start at the Estadio Municipal da Bela Vista, with Jen Beattie getting her head to a Caroline Weir free kick after just three minutes, but Sonný Þráinsdóttir saved comfortably.
Scotland took the lead on 13 minutes, Arnot finishing well from just inside the box following Kim Little’s corner.
Þráinsdóttir was called into action again midway through the first half, foiling Beattie once more from a set-piece.
On the half-hour mark, Cuthbert screwed a shot just wide, but made amends two minutes later, sweeping the ball past the ‘keeper after good work from Little and Emslie.
Just ten minutes into the second period, Scotland were three goals up, Little rifling home after the ball broke to her in the box.
Iceland responded, reducing the deficit just before the hour mark as Sara Gunnarsdóttir found the net from the edge of the box. Jón Þór Hauksson’s side threatened again on 63 minutes but the final effort hit the side-netting.
Arnot got her second, and Scotland’s fourth, on 66 minutes. Weir’s clever diagonal pass found the former Hibs Ladies striker and although her first shot was blocked, she crashed home the rebound to restore the three-goal advantage.
Substitute Zoe Ness, on for Cuthbert, nearly made it five on 74 minutes but pulled her shot wide of the target while Little forced Þráinsdóttir into action yet again on 87 minutes, the Breiðablik ‘keeper making a fine save.
Abi Harrison, on for former Hibs team-mate Arnot, had the ball in the back of the net with her first touch but the goal was chalked off for offside.
Scotland’s victory - all the more impressive given their defeat to Iceland in La Manga in January - sees them finish second in Group A.
They will face another second-placed side on Wednesday, with their opponent decided by the match between Poland and the Netherlands.
Scotland: Shannon Lynn, Kirsty Smith, Rachel Corsie (c), Jen Beattie, Kim Little, Caroline Weir, Leanne Crichton (Jo Love 71), Nicola Docherty (Hayley Lauder 87), Claire Emslie (Fiona Brown 61), Erin Cuthbert (Zoe Ness, 61), Lizzie Arnot (Abi Harrison 87). Subs not used: Lee Alexander, Jenna Fife, Chloe Arthur, Joelle Murray, Jane Ross, Christie Murray, Frankie Brown.