The result was their second away win following their round one triumph over Souths in Perth and last week's home victory over the Titans, while the luckless Raiders remain winless to start their campaign following consecutive 30-28 defeats to the Titans and Knights over the past fortnight.
The win also ends the Warriors four-game losing run against Canberra and gives them just their fourth win in 16 visits to the Australian capital.
Warriors coach Stephen Kearney was pleased with his side's character to claim a hard-fought win when they looked well below their best for the majority of the game.
"We didn't play particularly well and didn't give ourselves the best start but I still liked the effort and energy," Kearney said.
"They showed a tremendous amount of courage not to let the game get too far away from them and give themselves an opportunity with three minutes to go.
"We're going to enjoy the win. It's a special victory for the club and to come back like that to make it three in a row is good."
The Warriors were forced to defend for long periods with captain Roger Tuivasa-Sheck saving two tries while Luke prevented a third, but a lack of patience and poor execution meant they failed to capitalise on scoring chances.
Five penalties in the opening minutes put them under pressure and front-rower Adam Blair was sinbinned on the sixth occasion before the Raiders scored two quick tries to hooker Siliva Havili and second-rower Elliot Whitehead for a 12-0 lead after 10 minutes.
But poor goalline defence from the Raiders saw the Warriors strike back on their first attacking foray through centre Peta Hiku, before Canberra No7 Sam Williams kicked a field goal just before the break.
Left wing Nick Cotric got Canberra's third try soon after the resumption and captain Jarrod Croker kicked a penalty to put them 13 points clear, but the Warriors came back again with second-rower Tohu Harris scoring their second to help narrow the margin.
Their winning run looked certain to end before Luke darted from close range to set up a grandstand finish and they showed the tenacity and belief to clinch the result after all hope looked lost.
Tuivasa-Sheck said the gutsy nature of the win put it among the most memorable of his career.
"This is up there. Emotionally just having everything against us and the boys digging deep to fight back," he said.
"To come back and finish right at the end is massive for me and the team, the way we can fight through these games to get the win."
The Warriors will look to continue to their winning and claim a third away victory when they meet the Roosters in Sydney next Saturday, before hosting consecutive home games against the Cowboys and Broncos.
Warriors 20 (Peta Hiku, Tohu Harris, Issac Luke tries, Shaun Johnson 3/3 cons, 2 field goals)
Raiders 19 (Siliva Havili, Elliot Whitehead, Nick Cotric tries, Jarrod Croker 2/3 cons, 1 pen, Sam Williams field goal)
