7 October Wales are second in Group D, one point behind leaders Serbia and one ahead of third-placed Republic of Ireland with one game to play.
Chris Coleman’s side will qualify automatically for next summer’s tournament in Russia if they beat the Republic in Cardiff on Monday and Serbia fail to overcome Georgia.
Wales will finish at least second if they avoid defeat against Martin O’Neill’s side, a scenario which would leave them in contention for a play-off place.
The eight best second-placed teams from the nine groups enter the play-offs, and this victory puts Wales fifth in those rankings.
Victory in Tbilisi – the first time Wales have beaten Georgia – sets the stage for the Republic match, which is likely to be the most intense Wales international staged at the Cardiff City Stadium.
Wales’ starting line-up has seldom been harder to second guess in the absence of forward Gareth Bale, who is unavailable for this round of fixtures through injury.
For all the speculation about a first start for Liverpool teenager Ben Woodburn, or even a shock selection in Chelsea’s 17-year old Ethan Ampadu, Wales went for the tried and tested in Tbilisi.
Joe Ledley’s recall and a straight swap of Sam Vokes for Hal Robson-Kanu gave the visitors a familiar look, with Aaron Ramsey given a free role behind Vokes in Bale’s absence.
Celebrating his 50th cap, Ramsey was Wales’ most likely source of inspiration.
He might have given Wales the lead after just seven minutes, but fired wide from 12 yards after a burst of pace and a smart pass from Lawrence breached the Georgia defence.
Looking to attack with pace, Wales fashioned a chance for Andy King on 20 minutes, but Giorgi Loria was able to palm the ball to safety.
Another superb pass from Ramsey then again unlocked the hosts, but King wasted the opportunity.
Central to everything, Ramsey produced a peach of a pass on the half hour after King’s flick-on, but Vokes’ effort across goal drifted agonisingly wide of the far post.
Wales were dominant but might have trailed had Giorgi Kvilitaia not headed inches wide from their first real foray forward.
Since Wales have found themselves in a situation where every qualifier is essentially a must-win game, it has been the next generation who have come to the fore.
Woodburn’s heroics against Austria and Moldova were matched in Tbilisi by Wales’ least-capped first XI player, with Derby’s Lawrence providing the inspiration.
His big moment came 49 minutes into his ninth Wales appearance, as he collected the ball from Ramsey and powered a 20-yard effort through Loria’s grasp, the swerve and sheer velocity beating the goalkeeper, who perhaps should have done better.
Georgia simply could not contain Lawrence as he continuously cut in from the left, playing in an inverted wide role that allowed Ben Davies to provide width and contain the hosts’ naturally attacking full-backs.
Georgia were largely restricted to seeking set-pieces as they failed to muster a single effort on goal until the 80th minute on a night when keeper Wayne Hennessey was a virtual spectator.
When he was called into action, Hennessey kept Wales’ hopes alive, denying Giorgi Merebashvili after he cut inside and fired across goal with a little help from his captain Ashley Williams.
Wales got deeper and deeper in the final exchanges and were almost made to pay for losing possession, but last-ditch defending from Davies allowed them to clear their lines.
Lawrence will get the plaudits, but Ramsey was head and shoulders above the rest on a night when Wales most needed him.
Not only was he their best attacking outlet, but he showed why he used to be skipper as he barked instructions throughout and helped Wales to keep their shape in the last few, frantic moments.
Wales manager Chris Coleman, speaking to Sky Sports: “The players didn’t disappoint. It was a tough surface and we found it difficult at times.
“We made some great situations, which we didn’t always capitalise on – but the commitment from the lads was great.
“All we can do is work hard and take care of our business. We have a huge test on Monday against the Republic of Ireland. We have a gameplan and we will see where it takes us.
“It was always going to be tight in this group and I felt it would always go down to the last game.”
Wales midfielder Aaron Ramsey: “We found a way to break them down. We wanted to go back to Cardiff with three points and it will be a big game against Ireland on Monday now.
“We find a way and that is why this team is so special.
“We are halfway there. We wanted to finish with two wins. Hopefully we can give our fans something to cheer about on Monday.”