Durham captain Dale Benkenstein felt his side handled the pressure superbly after belatedly securing their place in the Twenty20 Cup finals day.
The Dynamos had expected to play Yorkshire in the quarter-finals a fortnight ago but finally progressed at the expense of Glamorgan following two changes of opponents.
Nottinghamshire were initially reinstated in Yorkshire's place after the White Rose were exposed for fielding an ineligible player but it was Glamorgan who finally earned the reprieve when judicial proceedings ended.
Glamorgan looked like making the most of their surprise chance at the Riverside as the Dynamos toiled early on in their innings but 55 in the final over saw them post 163 for eight and the basis for a 44-run win.
Benkenstein said: "You are always going to be under pressure in a game like this, we had been waiting quite a while to play.
"With the team we have got there is always massive expectations, but they were coming into the competition with nothing to lose.
"We always knew we were going to be in a fight and after about eight overs we were right in that fight.
"We got ourselves back on track, Will Smith batted brilliantly and we finished well. We took that right into the bowling."
Smith led the Dynamos recovery with 51, his half-century coming up off 37 balls with five fours and a six.
Glamorgan made a disastrous start in reply as Liam Plunkett removed Richard Grant and David Hemp in the first over on his way to figures of three for 16.
Jamie Dalrymple (32) and Mark Wallace (26) offered the Dragons hope but they eventually collapsed to 118 all out with Steve Harmison and Paul Collingwood claiming two wickets apiece.
Glamorgan skipper David Hemp said: "Obviously we are very disappointed we are not going to progress in the competition.
"The start we had with the ball ... even until the last five overs, we were in a very good position.
"But that is the beauty of Twenty20 competition, it can change in a couple of overs.
"Credit to Durham, they got themselves to 160 and that's always competitive."
Durham now play Middlesex in the second semi-final at the Rose Bowl on Saturday, with Kent and Essex opening the three-game showpiece.