The former Wigan and Derby acting manager has generated as new spirit and it has been reflected with the recent run of form.
It was Walsall's third successive win as they extended their unbeaten run to five games with second half goals from their two youngsters, Troy Deeney and Alex Nicholls.
Yeovil, on the other hand, are going through a bleak spell and have now collected only one point from their last four games and are dropping towards a relegation battle.
They were always off the pace against a Walsall side that is making a late bid for the play-offs.
In a generally low key first half neither side posed too many problems for each other. The closest Walsall came to opening their account was a wild shot over the bar by Dwayne Mattis.
Yeovil's reply was a powerful drive by Jon Worthington but Clayton Ince easily dealt with the effort.
Walsall finally created the breakthrough in the 52nd minute when Deeney latched onto a knock-on from Anthony Gerrard to beat Josh Wagnenaar to record his eighth goal of the season.
With Luke Rodgers struggling to find his goalscoring form Yeovil were unable to pose any real threat as Walsall dominated the midfield.
Sofiene Zaaboub, who has shown improved form under the guidance of Hutchings, was able to show his skill with some good runs.
But it was an accurate free-kick by Zaaboub which enabled Walsall to settle the match in the 76th minute when the unmarked Nicholls headed home the winger's cross.
Walsall were denied a third goal when a Mattis header from another Zaaboub cross smashed against the bar.
Yeovil, however, were unable to hit back despite Walsall losing their key defender, Gerrard, with a hamstring injury. The Saddlers switched Michael Ricketts into a defensive role and the former Bolton player emerged as a big asset.
Importantly, Walsall kept a clean sheet for the third successive match and moved closer to their target of the play-offs, with Hutchings increasingly confident that the Saddlers can clinch the sixth spot.