After 33-30 in Linköping on Wednesday, Sweden now won 31-30 in Andalusian Jaén.
The home team had two opportunities to equalize at the end, but Tobias Thulin saved both times and ensured that Sweden took their fourth straight victory in the EHF Euro Cup.
Sweden took command after just a couple of minutes and then led the whole match.
At most, the lead was six goals, but the Spaniards crept closer at the end.
Top scorers forward in Blågult were Felix Claar and Emil Mellegård, both seven-goal shooters.
Sweden, who lost the bronze match in the home World Cup against Spain, tops the table in the EHF Euro Cup ahead of the two final matches against Germany (Kristianstad, April 27) and the world champions from Denmark (Herning, April 29).
Denmark are two points behind and the only team that can challenge for victory in the tournament, which will be played with the four countries already directly qualified for next year's European Championships in Germany.