Italy took the lead when just under 20 minutes were played.
Olivia Schough was the scorer. Valentina Giacinti made it 1-0.
Sweden made a better second half, but the score stood until the 70th minute when substitute Lina Hurtig was sent off and Sweden got a penalty.
Caroline Seger, also replaced, had to step forward and unlike in the Olympic final, the ball went in.
Italian missed open goal
With only six minutes left of regular playing time, Arianna Caruso got a perfect position to decide when she would nod the ball into the open goal from close range.
But she managed to hit the crossbar and covered her face after the miss.
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Is this this year's miss?
In the penalty shootout, Seger started by setting her penalty and the final Swedish penalty was actually set by goalkeeper Hedvig Lindahl when she thundered it in.
Then she saved Annamaria Serturini's penalty and then it was decided.
- Funny that we got the win in the end.
I'm very impressed with the girls who took penalties.
I do not think that all focus should be on me just because I scored a goal.
There were many good efforts in a fairly newly composed team, says Lindahl.
- I think Sweden is the better team over 90 minutes.
They deserved it, says SVT Sports expert Daniel Nannskog.
First Algarve victory since 2018
The Swedes had only played one match earlier in the tournament when they beat Portugal 4-0.
They got a walk over victory against Denmark due to covid-19 among the opponents.
They had completely different starting elves in the two matches.
The last time Sweden won the Algarve Cup was in 2018, but then they shared the victory with the Netherlands after the final had rained away.
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Here Seger settles for a penalty