|Wales' Tom Lawrence controls the ball next to Georgia's Otar Kakabadze during their FIFA World Cup 2018 qualification match in Tbilisi on Oct 6, 2017. (Photo: AFP/Alexander Nemenov)|
Lawrence lashed home right-footed from just outside the area in the 49th minute to earn Wales only their fourth victory in nine qualifying games and put them clear in second spot in Group D with 17 points, a point behind leaders Serbia.
Should third-placed Ireland suffer a shock home defeat by Moldova later on Friday Wales would be guaranteed at least runners-up spot in the group and a possible playoff place as they bid to reach the World Cup for the first time since 1958.
Serbia are in action at fourth-placed Austria where victory will see them finish as group winners and qualify for the finals.
Wales, who are without injured talisman Gareth Bale, face Ireland on Monday in what is shaping up to be a colossal match with a likely playoff spot up for grabs.
"I always knew this was going to be a tight group and always thought it would go the wire," Wales manager Chris Coleman said.
"All we can do is work hard and take care of our business. We have a huge test on Monday night against the Republic of Ireland. We have a game plan and we will see where it takes us."
Only the eight runners-up with the best records from the nine European groups will take part in the two-legged playoffs.
Wales were ninth best going into the match in Tbilisi but victory lifted them to sixth in that complex table.
Without Bale, Wales produced a disciplined performance against a tricky Georgian side who drew 1-1 in Cardiff - one of five draws for Coleman's team.
Chances were few and far between but Derby County's Lawrence produced a quality finish to break the deadlock.
Turning into space 30 metres out he advanced before firing a powerful drive across Georgia keeper Giorgi Loria.
There were nerves at the end as Georgia pressed for an equaliser - their best chance coming when a superb pass sliced open the Welsh defence to leave Otar Kakabadze in the clear but he elected to cross rather than shoot and wasted the chance.