Confidence was high of Larsson getting his nation onto the medal table, given that the 25-year-old set the world leading time of 6.54 seconds in Dusseldorf last month.
Larsson had put in two consistent runs earlier in the competition to book himself a place in the final, beginning with a win in his Heat in a time of 6.59 seconds.
In the Semi-finals, he went a shade quicker - 6.58 seconds - to finish second behind Great Britain's Andrew Robertson as the fourth fastest of the eight qualifiers.
His start in the Final, however, was not the cleanest, but he quickly got into his stride to force his way through the field.
He was able to pip bronze medallist Robertson on the line this time, recording a new Swedish national record of 6.52 seconds.
That was not quite enough to beat the winner, Great Britain's Jeremiah Azu, who set a new world leading time of 6.49 seconds to claim his nation's first gold in Apeldoorn.
It is a second major medal for Larsson, who improved on the bronze he took in this event in Istanbul two years ago before finishing fifth at 2024's World Indoor Championships in Glasgow.
Elsewhere for Sweden, Andreas Almgren recorded the second fastest time in the Heats of the men's 3000m and thus will run in Sunday afternoon's Final.
However, Linn Söderholm failed to advance from the the Heats in the women's competition over the same distance.
Meanwhile, Wilma Nielsen narrowly missed out on a place in the women's 800m Final, finishing fourth in the second Semi-final.