Strauss, full of confidence after his century in the victory at Old Trafford, took his team calmly to 84-2 at lunch, but in the first over after the interval edged a very wide delivery high to first slip.
Captain Phil Vickery - who made his England debut as a replacement at the Stade de France 10 years ago - praised his side's dedication in grinding out a confidence-boosting victory.
Styria's governor, Waltraud Klasnic, a member of the People's Party, said her party's victory was a vote of confidence for the conservatives' policies in the region.