Stewart scored the only goal of the game in Luxembourg.
Ipswich ruled the game
Ipswich dominated the game but struggled to push through.
They reached the third round of the competition last season.
Ipswich looked like they might be disappointed when they had a first-minute Thomas Gaardsoe goal disallowed.
But Stewart's 90th minute volley finally beat Kevin Hartet to clinch a last-gasp win.