The 22-year-old was deployed as a left wing-back by Wales boss Robert Page, after earning his first international cap in last week's 2-2 draw with the Czech Republic.
The Welsh are third in Group E, level on points with the second-placed Czechs. Page's side have played a game fewer, leaving their hopes of securing second spot in their own hands.
Leeds United forward Daniel James, who scored the equaliser in last week's 2-2 draw, was also among the starting 11 in Tallinn.
The decisive goal arrived early in the first half after former Barnsley and Rotherham United striker Kieffer Moore poked home after being in the right place at the right time following a goalmouth scramble.
It was a hard-fought contest with Danny Ward pulling off some smart saves to ensure Wales left Estonia with maximum points.
Page's men face Belarus and Belgium in their final two fixtures. Both games are at home next month, with four points enough to help them to second place and a World Cup play-off spot.