The 17-year-old midfielder netted midway through the second half to put the visiting team ahead at Solihull Moors’ Armco Arena.
Brad Burrowes had earlier scored a penalty to cancel out Ollie Bostock’s spot-kick opener for the Baggies.
After Lynskey had put Villa in front, substitute Rodrigo Fortes made the points safe when he pounced on a defensive mistake to score a third.
Both teams had gone into the match seeking their first points of the season after defeats in their opening matches.
Villa, managed by former Albion interim boss Jimmy Shan, made a positive start but it was the Baggies who went in front from the spot. Mohamed Kone brought down Akeel Higgins in the box and Bostock just beat the dive of visiting keeper Ronnie Hollingshead.
The advantage did not last long, however. Travis Patterson was caught inside the area by Jamal Mohammed and Burrowes blasted home his spot-kick to draw Villa level.
A neat passing move then saw them take the lead in the 66th minute. Substitute Trai-Varn Mulley found the run of Aiden Borland and his hook across goal was converted by Lynskey at close range.
With the Baggies pushing for a leveller, a poor touch by Michael Parker then allowed Fortes to race through on goal to score the third.
Mulley should then have added a fourth in stoppage time but skied his effort over the bar after excellent work by Lynskey.