The Welsh county secured a spot in the showpiece game on September 21 by overcoming reigning champions Hampshire by 31 runs at The Ageas Bowl.
Glamorgan's Jim Allenby (74) and Ben Wright (47) blasted 57 runs of the last four overs of their innings - and 37 from the final two - to post the Royals a target of 235.
But the home side - for whom Dimitri Mascarenhas was playing his final game in one-day colours - could only make 203-8 in reply, meaning they matched their semi-final exit from this term's Friends Life20 tournament.
Fraser, Middlesex's Director of Cricket, believes Hampshire may rue fielding after winning the toss in Southampton, but says the hosts were "out-disciplined" by Glamorgan, who can now look forward to their first Lord's final in 13 years.
"We can look at Hampshire's decision at the toss but Glamorgan won this game in the last four overs of their batting innings thanks to some wonderful hitting from Wright and Allenby," the former England paceman told Sky Sports.
"However, they were also excellent in the field; they were organised, knew what they were about and out-disciplined Hampshire, albeit on a slow, low pitch that suited their line-up.
"Glamorgan haven't had many games like this in recent times, but they rose to the challenge and have a very capable one-day side."
Australian-born all-rounder Allenby - who penned a new four-year deal with the SWALEC Stadium outfit in August - backed up his 71-ball 74 by shipping just 18 runs and claiming two wickets from his bowling quota of eight overs against Hampshire.
And Fraser - whose Middlesex charges were eliminated at the YB40 group stage - believes the ex-Leicestershire star's ability with bat and ball means he will no longer slip under the radar.
"Allenby is a very good cricketer and I'm sure Glamorgan will be delighted he has signed a new contract because I think there were quite a few counties sniffing around," he added.
"He is not a huge, destructive hitter but he is an effortless timer of the ball and keeps getting it away for four. He has a very good cricket head on him and he knows how to bowl straight, too.
"He is easy to underestimate but I don't think people will be underestimating him anymore."