The Leeds United winger produced a pinpoint finish into the bottom corner after being put through on goal by Harry Wilson after goalkeeper Danny Ward had scored a spectacular own goal four minutes into the second half.
The ball was played back to the Leicester City goalkeeper who failed to control the pass as he the ball trickled into the bottom corner.
The sides were level at the break after Aaron Ramsey had put Wales ahead with 36 minutes gone before Jakub Pesek equalised just two minutes later.
Huddersfield Town's Sorba Thomas replaced Liverpool's Neco Williams to make his international debut on 76 minutes, helping Wales see out the game to earn a point.
The result leaves Wales third in their World Cup qualifying group, level on points with the second-placed Czechs with Rob Page's men having played one game fewer.
Meanwhile in Group H, Middlesbrough's Andraz Sporar scored his first goal in World Cup qualifying to help Slovenia to a 4-0 win over Malta.
The Boro man struck five minutes into the second half to put his side 2-0 ahead after Josep Ilicic had opened the scoring in the first half.
Ilicic netted Slovenia's third before substitute Benjamin Sesko rounded off the scoring to put Slovenia into third place.
Elsewhere, Boro's James Lea Siliki came off the bench to help Cameroon pick up an important 3-1 World Cup qualifying victory against Mozambique.
In the Under-21s ranks, Rotherham United' s Joshua Kayode scored for the Republic of Ireland as they claimed a 2-0 win over Luxembourg.
Doncaster Rovers' on-loan midfielder Ethan Galbraith captained Northern Ireland Under-21s as they were edged out 1-0 by Russia.