Alex Rodman and Abu Ogogo scored the goals as Paul Hurst’s high-flying side added three more points to their tally.
Shrewsbury were rewarded for a bright start with a sixth-minute breakthrough as Rodman converted Jon Nolan’s inviting low cross from the right.
The hosts nearly added to their lead shortly afterwards but Carlton Morris struck the post from Shaun Whalley’s cross.
Then the influential Nolan hammered a powerful 20-yard drive over the bar.
Walsall were also lively going forward and Dean Henderson, the Shrewsbury goalkeeper, had to be alert to tip a Kieron Morris header over the bar.
Nicky Devlin then went close to an equaliser when he burst into the box and fired against the near post from a narrow angle before Erhun Oztumer was off-target from a 25-yard free kick.
Walsall’s Liam Leahy headed against the woodwork in the closing stages before Shrewsbury doubled their lead in the 88th minute as skipper Ogogo swept home Rodman’s cross from the right.
Pivotal game in Group E almost a pick ‘em with the bookies