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Needing a win to avoid relegation from Group A3, the victory keeps Sweden's survival hopes alive as they head into their final group game against France in Paris on Wednesday, despite still being bottom of the group.
Sweden boss Janne Andersson had to watch the game from home following a positive test for COVID-19 and 20-year-old forward Kulusevksi was chosen to start up front with Marcus Berg.
The decision paid off quickly as the Juventus player had a stinging shot saved and created another chance for winger Emil Forsberg. He gave his side the lead when he held off Mateo Kovacic to side-foot home his first goal for his country in the 36th minute.
Danielsson made it two in first-half stoppage time, swooping in at the near post to send Sebastian Larsson's corner flying into the net with a glancing header to cap Sweden's best 45 minutes of the competition so far.
They continued to dominate in the second half but Croatia muscled their way back into the game and pulled a goal back when an Ivan Perisic header deflected off Danielsson and into the net.
The tall defender almost made amends late on with another towering header from another set piece, but keeper Dominik Livakovic was able to keep his shot out.
The win leaves Sweden bottom of the group on three points, with the Croatians third on goal difference.