It was man-of-the-match Walters’ seventh goal for his country which made it seven wins from seven against Georgia for Ireland.
The result, coupled to world champions Germany winning 3-2 against Scotland at Hampden Park, now means that Martin O’Neill’s Ireland have consolidated third place - which guarantees at least a play-off - in Group D, four points ahead of the Scots.
In the evening’s other game, Poland beat Gibraltar 8-1 in Warsaw to remain second in the group, two points ahead of Ireland.
Next up for Ireland is a visit to Dublin of Germany next month before the group campaign ends with a trip to Poland.
Ireland manager O’Neill made just one change from the side that beat Gibraltar 4-0 last Friday night in Faro with Seamus Coleman, recovered from a hamstring injury, coming back in at right-back for Cyrus Christie.
Georgia boss, Kakhaber Tskhadadze, who celebrated his 47th birthday on the night, also made only one switch from their inspiring win over Scotland the same night as Zurab Khizanishvili came into their defence in place of the injured Jano Ananidze.
Ireland began brightly with skipper Robbie Keane volleying over the bar on six minutes after Wes Hoolahan picked him out having worked a clever one-two with Walters.
Buoyed by their win over Scotland, Georgia didn’t lack in confidence, though, and Ciaran Clark had to make an important block to deflect Levan Mchedlidze’s angled drive away from goal three minutes later.
The visitors got in behind Ireland again within two minutes. Valeri Kazaishvili threaded a ball through for the run of the lively Mchedlidze whose weak shot didn’t trouble Shay Given.
Though Ireland enjoyed good possession, they coughed up another chance on 24 minutes, Tornike Okriashvili’s overhead kick from a Giorgi Navalovsky cross on the left bouncing wide for another let-off.
The Irish crowd weren’t really lifted until their side’s best chance of the first half on 37 minutes.
Hoolahan’s cross was headed away by a defender. But the ball dropped to Coleman on the edge of the area and, having teed it up, the right-back hit a crisp volley that Nukri Revishvili batted away for Ireland’s third corner of the match.
Needing to add more tempo to their game, O’Neill brought Shane Long in to replace Keane for the second half.
But it was 12 minutes in before Ireland troubled the Georgian defence. Coleman was involved again, getting the ball back from Hoolahan as he raced into the area. The toe-poked shot lacked conviction, however, as it trickled through to Revishvili.
That was the impetuous for Ireland’s first real sustained - and telling - spell of pressure in the match.
Jeff Hendrick’s deflected shot brought an awkward save from Revishvili before Walters’ flicked header from Glenn Whelan’s ball into the area ran through to the Georgian keeper.
James McCarthy then might have shown more composure as he blazed a shot over the top after Revishvili punched away a cross from Robbie Brady.
The pressure from Ireland finally told on 69 minutes. Terrific footwork by Hendrick on the left produced a mazy dribble past three Georgian defenders before he crossed for Walters to bundle the ball to the net from just yards out.
The one blot on the night arrived with yellow cards given in quick succession to Whelan and substitute James McClean, meaning they are now suspended for next month’s home clash with the Germans.
Both were then involved in a guilt-edged chance for Ireland to double their lead on 77 minutes.
Whelan pounced on a mistake to set up McClean to cross with Long just unable to apply the crucial touch at the near post.
McClean almost added a second goal for Ireland two minutes into added time. Cutting in from the right, the winger unleashed a stinging left-foot drive that Revishvili clawed away with his left hand.
Republic of Ireland: Given; Coleman, O’Shea, Clark, Brady; McCarthy, Whelan, Hoolahan (McClean, 75), Hendrick; Walters, Keane (Long, h/t).
Georgia: Revishvili; Kverkvelia, Amisulashvili, Khizanishvili (Kenia, 81); Lobzhanidze, Kashia (Tsintsadze, 76), Kankava, Navalovsky; Kazaishvili (Papunashvili, 64), Okriashvili; Mchedlidze.
Referee: István Vad (Hungary).