The first goal came after a successful substitution by new coach Jens Gustafsson.
After just 43 seconds on the pitch, Mikkel Rygaard Jensen set up Layouni, who was completely unmarked after a rush into the penalty area and could score the 1-0 goal with his left foot.
Then Layouni struck again in the 94th minute and sealed the match after a BP-forcing.
Layouni is a nightmare for BP, as the Häcken forward has now scored six goals against the Stockholm team.
Brommapojkarna, however, had their chances.
Already in the opening, Victor Lind hit both posts behind home goalkeeper Andreas Linde.
It was so close, I was ready to celebrate, says Lind in the halftime interview.
Lind then had a huge opportunity with ten minutes left, but Häcken goalkeeper Linde won the duel and could steer the shot over the crossbar.
Finally, home player Silas Andersen could save twice on the goal line in stoppage time before Layouni scored in the counter-attack and made it 2-0.
Häcken's three-point start in the Allsvenskan comes after the team also reached the final in the Swedish Cup, where Malmö awaits in the final away in late May.
But not everything was to Häcken's satisfaction, as new defender Leo Väisänen had to leave the pitch with an injury after just eleven minutes of play. He was substituted in in the 72nd minute and had to leave again in the 83rd.
