Wales will likely play either Argentina or Japan in the knockout stages after another accomplished display in which they led 17-7 at halftime but had to withstand a Georgian rally in the second period.
They scored other tries through prop Tomas Francis, full-back Liam Williams and centre George North, and gained revenge for a shock 13-12 loss to Georgia in Cardiff last November, a result that hastened the exit of former coach Wayne Pivac.
Georgia go home without a win but have been competitive and managed an 18-18 draw with Portugal. Their tries came from captain Merab Sharikadze, hooker Vano Karkadze and wing Davit Niniashvili.
"We spoke in the week about being quite ruthless," Wales captain Dewi Lake said.
"We dropped off a bit at the end of the first half and the start of the second half and Georgia came back at us.
"We picked it up in the final 20 and we scored some nice tries and played some nice rugby."
Injury concerns
Wales lost fly-half Gareth Anscombe in the warm-up with a groin injury that puts the remainder of his tournament under threat. With Dan Biggar having been forced off against Australia in their previous fixture, they could suddenly be light in the number 10 jersey.
The sight of number eight Taulupe Faletau heading straight down the tunnel for medical treatment to his chest will also be a worry for coach Warren Gatland.
Wales scored their opening try when they set up a driving maul from a line-out and Francis barged over as they spun the ball into the midfield.
Williams scored his 20th try for his country when they launched from another attacking lineout and spun the ball wide, with the full-back able to dance his way over the line.
Georgia captain Sharikadze became the first player to score a try against Wales in three tests when he finished a concerted spell of pressure, going over under the posts after numerous phases.
Wales extended their advantage after half-time as Rees-Zammit raced clear and he had too much pace on the outside for the retreating Georgian defence.
They looked virtually home and dry at that point, but Georgia fought back and scored the next two tries, the first a close-range finish from Karkadze before Niniashvili ghosted through a massive gap in the Welsh defensive line to bring the score to 24-19.
Wales took control again, however, when Williams’ chipped kick was perfect for Rees-Zammit to score his second, before he added a third and turned provider for North to seal a strong performance.
"I’m a little bit disappointed because we didn’t achieve our target (of winning a game), but one thing I can say is we played well against tier-one countries every game," Georgia coach Levan Maisashvili said.
"Results were not what we want, but we played well in every game and never gave up."