Basel have won the Swiss Super League for the last three seasons and, in addition to Wednesday's triumph, they also claimed the Cup in 2010.
Only Sion's Cup win last season denied them a hat-trick of doubles.
Rank outsiders Luzern, whose last title was 30 years ago when they won the cup, looked sharper in the first half when they created several chances but failed to take them.
Basel were more clinical and went ahead 10 minutes after halftime when Benjamin Huggel was left unmarked and headed in from six metres.
Croatian defender Tomislav Puljic levelled 12 minutes later with another header after he was also left unmarked at a corner.
Basel goalkeeper Yann Sommer was the hero in the shootout as he saved spot-kicks from Moshe Ohayon and Florian Stahel to give his side a 4-2 win on penalties.
Basel coach Heiko Vogel has yet to lose a domestic match since taking over in mid-October, Wednesday's result taking his unbeaten run to 26 matches.
His only defeats have been in the Champions League against Benfica and Bayern Munich, although the latter was an emphatic 7-0 reverse.
Basel have won the cup 11 times and the double five times.
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