The Dwars, which means 'Across Flanders', is one of the main build-up races ahead of the Spring Classics, which begin on Friday with E3 Harelbeke.
Wallays was part of a four-man breakaway but he distanced his companions just before the finish to cross the line alone.
His compatriot and Topsport Vlaanderen team-mate Edward Theuns won a sprint for second ahead of another Belgian Dylan van Baarle, with Poland's Kwiatkowski fourth.
The Pole is one of the favourites for the three Ardennes Classics in the second half of April.
Before then the main attention will be on the Tour of Flanders on April 5 and Paris-Roubaix a week later.
The Dwars is one of the six co-operating races known as the Flanders Classics, of which the Tour of Flanders is the most important.