Saturday’s 23-run win over Oman, coupled with other results, meant the Scots came from behind to clinch top spot in Group B.
They will take their place at the global event in India as well as going through to the semi-final of the qualifying tournament.
Coach Bradburn, whose team had to recover from morale-denting defeats by Holland and Afghanistan early in their campaign, heaped praise on his entire 15-man squad after they pipped the Dutch by just 0.054 of a run.
He said: “I don’t normally single anyone out but if there is one person it is skipper Preston Mommsen.
“He has grown as a leader and a cricketer and he wears the captaincy well.
“Preston leads from the front and his performances with the bat have been exceptional. He has often come in when we’ve needed quick runs and he has brought his skills to the fore.
“I am very proud of the way he has developed his game and his captaincy.”
Kiwi Bradburn, who recently celebrated a year in charge, added: “All 15 of the guys deserve enormous credit. We’ve had to select horses for courses and every one of the players has accepted that the team’s needs come before individual ones.”
Mommsen, who has the second best strike-rate in the tournament, was again a key figure on Saturday, scoring his 32 from only 18 balls as the Scots, having been given a marvellous start by Kyle Coetzer’s 63, took the game away from Oman at storm-battered Goldenacre.
Safyaan Sharif then claimed three wickets while Ali Evans became the leading wicket-taker in Group B with another two.
With Afghanistan denied the chance to win the group when their clash with Canada at Stirling was abandoned, it put Scotland in pole position for automatic qualification.
However, the drama was only beginning because attention then turned to Myreside where Kenya and the Netherlands had unfinished business in the day’s late match.
Victory for Kenya would have taken them to the top while Holland could also squeeze out Scotland by chasing 98 runs in 7.4 overs.
The Dutch were on course to do just that until a flurry of wickets stalled them and they achieved their target five balls too late.
“We were sweating on every ball,” revealed Bradburn, whose side watched events unfold while huddled round several laptop computers in their team hotel.
“It was a horrible way to watch and some laptops were refreshing quicker than others, but we got there in the end and it was very, very emotional.”
Scotland will learn their opponents for Saturday’s semi-final tomorrow and Bradburn would relish another clash with Afghanistan.
“They are a quality side and they beat us well last week,”said Bradburn.
“But we’d relish the opportunity to perhaps play them again next week.
“We all know that we haven’t quite put all three disciplines together yet.
“We can definitely still improve so that makes it extra pleasing to have come top of such a tough group.”