In the season's third meet of 14, Norman stomped home in the 400m and Rio bronze medallist Asher-Smith eased to victory over Olympic and world champions in the 200m.
Michael Norman wins 400m in Stockholm
It was all eyes on Norman as the 21-year-old ran his first ever 400m at an IAAF Diamond League meeting.
He didn't disappoint.
The USA's rising star clocking 44.53 to win the race ahead of training partner and 400m hurdles specialist Rai Benjamin (45.13) in second and Michael Cherry (46.30) third.
- Michael Norman 44.53
- Rai Benjamin 45.13
- Michael Cherry 46.30
Vernon Norwood finished fourth giving the USA the top four finishes.
In the lead up to the race there was much talk about Norman taking Wayde van Niekerk's 43.62 Diamond League record from Lausanne 2017.
Norman had, after all, run a 43.45 in Torrence, California in his season opener but reports of a gusty headwind may have hampered his record-breaking ambitions.
But there were no excuses from Norman who wasn't pleased with the result.
"Today was challenging, both mentally and physically - and there's a lot of things I need to work on. I'm not particulary satisfied with my race." - Michael Norman
"I need to work on the second part of the race still," he continued, "and I'll readjust and reevaluate as I go."
"A long way to worlds just yet. I'll continue working hard with my coach, and we'll see where that gets me."
Dina Asher-Smith takes women's 200m
Britain's Dina Asher-Smith wins the 200m Diamond League meet in Stockholm 2019 with a world-leading time of 22.18.
Reigning Olympic champion Elaine Thompson looked like she was regaining her best form after her 200m victory in Nanjing last week in 22.40.
2-time world champ Dafne Schippers also felt that she was in with a shout.
But neither the Jamaican or the Dutchwoman proved a match for a determined Dina Asher-Smith.
Britain's track star pulled away on the home straight, and eased to victory.
"I am happy with that. My aim was to come, win and run my own race which is very important in a race of that calibre." - Dina Asher-Smith
- Dina Asher Smith 22.18
- Elaine Thompson 22.16
- Dafne Schippers 22.78
Asher-Smith continues her fine form after she opened season in style with victory in Doha in 22.26 and winning European gold in 21.89.
"I was very happy to win but I didn't expect to run that kind of time as it is quite cold out and late at night," Asher said after the race, "I didn't know my mum would be here - she tends to just turn up so when I saw her I was so happy."
"Next week is Rome Diamond League then I will be back to solid training."
Juan Miguel Echevarria settles for second
Local favourite Thobias Montler took the men's long jump with an 8.22m leap - a personal best for the Swede.
Cuban long jumper Juan Miguel Echevarria hit the headlines at this event last year when he nearly cleared the pit with an 8.83m jump (aided by 2.1m/s tailwind).
An 8.12m jump saw him take second here in Stockholm.
Cuban 1-2 in women's discus
Two-time Olympic champion Sandra Perkovic was competing for the first time since tasting a surprise defeat at the IAAF Continental Cup in Ostrava last September, and but it wasn't a triumphant return.
The Croatian finished 5th with Cuban rivals Denia Caballero and Yaime Perez dominating in first and second.
Timothy Cheruyiot wins men's 1500m for 9th time
It was nine times a charm for Kenyan Timothy Cheruyiot as he took his 9th Diamond League 1500m title in Stockholm.
The 23-year-old battled the cold and went one better than he did in Doha.
"I'm happy with today because I won. In Doha I was second but today I´m number one. It was cold but I tried my best. It was quick, almost 1:52 in 800m, that's fast." - Timothy Cheruiyot
Jakob Ingebrigsten 3rd
Exciting young Norwegian talent Jakob Ingebrigsten took 3rd and secured a podium finish.
The 18-year-old bettered his brother Henrik who finished in 9th.
"I was a lot more nervous beforehand because it was my first race of the season so I wasn't sure what shape I would be in," said the younger Ingebrigsten after the race.
"It was a great race for me and a great way to start my outdoor season." - Jakob Ingebrigsten
"Last year in Monaco I was one hundredth of a second in front of Souleiman, and today one hundredth behind. I think this season will be great."
"I had no expectations coming into today but now I am really looking forward to the rest of my races this season."
The next Diamond League stop will take place in Rome on 6 June with the traditional 'Golden Gala'.