Having conceded three tries in the opening quarter, the Lions fought back to level the match with a last-minute score from Leicester wing Austin Healey. It was then left to Healey's England colleague Matt Dawson to slot the match-winning conversion and move from villain to hero following the publication of a newspaper column which had been outwardly critical of the 2001 tour.
"The ACT game was a game and-a-half," says Morris, who appeared in six of the 10 tour fixtures.
"We had a massive team spirit in the camp and I think that shone through on that evening more than on other games. It was a self-belief.
"We went in at half-time had a good look at ourselves. There was nowhere for anyone to hide and we came out in the second half and put our heads on the block.
"Thankfully, we did it, and to win it with the last kick of the game was quite apt for the tour."
Matt Dawson kicked a match-winning conversion against ACT Brumbies
Unsurprisingly, Morris has fond memories of the match, particularly when you consider the talent on display in the ACT side.
The Brumbies went into the game as the newly crowned champions of the Super 12, with a backline that featured the likes of Mark Bartholomeusz, Graeme Bond and Pat Howard and a forward pack containing Justin Harrison, Dan Vickerman, Adam Freier and Radike Samo.
"It was actually a very cold night but a very fast game. We were hit cold.
"ACT have always been one of the form sides in whatever competition they're in. They had a lot of quality players and they were very well drilled side.
"They came out of the blocks and they scored three quick tries, with Pat Howard as the main orchestrator of that.
"I think we were 20-odd points down after 20 minutes so we all thought, 'hang on a minute now!' But we all gathered round and we came back."
For Morris, the game was not only a squad success but also a huge personal achievement having been overlooked for selection for the first Test in Brisbane.
The Welsh international capped a fine individual performance by supplying the final pass for Healey's sensational late score as he forced his way on to the replacements' bench for both the second and third Tests in Melbourne and Sydney respectively.
"I was in the right place at the right time for Austin's try," he says modestly.
"Big Jim Williams and I bounced off each other and I gave a pass out the back door to Austin Healey to go over in the corner. For Matt Dawson to then kick that goal, you couldn't have written it better yourself.
"To get over the disappointment of not being involved in the first Test and force my way back into the reckoning for the final Test was one of those moments you cherish."
Darren Morris supplied the pass that set up Austin Healey's second try
Morris earned his call up to the 2001 touring party after a solid international season with Wales, although he admits the way in which he learnt of his place on the plane was still a huge surprise and an even bigger honour.
"We had a reasonably successful Six Nations, bar the first game when we lost to England. After that we clicked together and played some good games.
"We went to Italy and nothing was said out there but we won quite well. We had a quiet evening then and came back with fingers crossed.
"I was doing some rehab early one morning and it came up on the TV. When I came home then, the envelope was there.
"I was very excited and I was inundated with phone calls and congratulations. It was a really exciting time, a new challenge and I was looking forward to it and wanted to be part of something special.
"It was the ultimate, ultimate honour. It's a great honour playing for your country and another great honour then to represent the British and Irish Lions going to Australia. It was an immense feeling and running out for the first game was superb. It was a dream come true in a way."