Morgan's co-captain Dewi Lake will skipper the side from hooker, packing down in a front row also comprising props Gareth Thomas and Tomas Francis.
No. 8 Taulupe Faletau and winger Louis Rees-Zammit are named in the match-day XV for a fourth successive time as Wales seek to round out their pool play with four wins from four.
They opened with a 32-26 victory over Fiji before seeing off Portugal 28-8 and sailing past Australia 40-6.
They will be wary, however, of a Georgia side that edged Wales 13-12 in Cardiff in November 2022, albeit the Georgians are yet to win in France after a 35-15 loss to Australia, an 18-18 draw with Portugal and a 17-12 defeat by Fiji.
"We want to win the game," Wales attack coach Alex King said. "We want to carry on (what we have been doing) over the last four weeks.
"We understand the threat Georgia pose after meeting in Cardiff 11 months ago, the performance they put in against Fiji on the weekend. They will be absolutely firing at the weekend that is for sure."
Tommy Reffell returns at openside flanker in six changes from the side that beat the Wallabies.
Aaron Wainwright is named at blindside while Dafydd Jenkins and Will Rowlands pair up in the second row.
Gareth Anscombe, who kicked a Welsh World Cup record-equalling 23 points against Australia, starts at fly-half, with Tomos Williams at scrum-half.
Playmaker Dan Biggar, King said, was continuing his recovery from a chest injury.
"He is just getting his recovery in after his slight injury. He is in the recovery stage and it's important he gets back ready for the quarter-final," said King, a former England fly-half who played under Wales coach Warren Gatland at Wasps before going on to earn his own coaching spurs at Clermont, Northampton, Montpellier and Gloucester.
"Anscombe was great after coming on after nine minutes. If something happens in the game it shows the guys on the bench have an important role to be ready to go straight away and even the guys who aren't in the 23.
"If something happens between Monday and the weekend you have to know your role and be able to step in at a moment's notice. The strength of this squad is the 33, it's not just the 15 who start."
Williams was preferred to Gareth Davies at scrum-half, King explaining: "We are just managing his load. He did an enormous amount of work, just making sure he is alright for the weekend."
Nick Tompkins and George North continue in midfield, with Rees-Zammit joined in the back three by Rio Dyer and full-back Liam Williams.
Forward cover on the bench comes in the form of Elliot Dee, Nicky Smith, Henry Thomas, Christ Tshiunza and Taine Basham, as Gareth Davies, Sam Costelow and Mason Grady offer backline coverage.
Wales (15-1)
Liam Williams; Louis Rees-Zammit, George North, Nick Tompkins, Rio Dyer; Gareth Anscombe, Tomos Williams; Taulupe Faletau, Tommy Reffell, Aaron Wainwright; Dafydd Jenkins, Will Rowlands; Tomas Francis, Dewi Lake (capt), Gareth Thomas
Replacements: Elliot Dee, Nicky Smith, Henry Thomas, Christ Tshiunza, Taine Basham, Gareth Davies, Sam Costelow, Mason Grady
