The Austrian champions, coached by former Italy boss Giovanni Trapattoni and bankrolled by energy-drink mogul Dietrich Mateschitz, should have little trouble wrapping up the tie in next week's second leg.
A brace from livewire Burkina Faso striker Yssouf Kone and a penalty from former Tottenham Hotspur striker Steffen Iversen also gave Norwegian title holders Rosenborg a healthy 3-1 away victory at Kazakhstan's FC Astana.
Dinamo Zagreb beat Slovenian side Domzale 2-1 away but 1991 European Cup winners Red Star Belgrade have more work to do if they are to reach August's third round, which will include big guns such as Liverpool and Lazio.
Serbia winger Ognjen Koroman netted with a swivelling shot from 25 metres after side-stepping a defender to grab the only goal as Red Star beat Estonia's Levadia Tallinn 1-0 at home.
Besiktas also stuttered to a 1-0 win over Moldova's Sheriff in Istanbul while Slavia Prague were held to a goalless draw over the border at Slovakia's Zilina, who beat Luxembourg's Dudelange 7-5 on aggregate in July's first round.
Seven other first leg ties were played on Tuesday with the return legs all taking place next week.