Elsewhere, Arsenal powered past Ostersund 3-0, Atletico Madrid thrashed Copenhagen 4-1 and Italian league leader Napoli slipped to a surprise 3-1 home defeat against Leipzig.
Batshuayi, who has been in sparkling form since joining from Chelsea on loan in the mid-season transfer window, helped host Dortmund record its first victory in European competition this season.
Dortmund hadnt won in eight previous appearances and only joined the Europa League after finishing third in its Champions League group. Andre Schurrle put Dortmund ahead after 30 minutes, only for Josep Ilicic to score twice for the Italian visitors in the 51st and 56th.
"Michy is a real goal-scorer, it was a good move to bring him here," Dortmund manager Peter Stoeger said. "Things are looking good. He is well liked, fully integrated and our goals and his personal goals align."
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NO TURF TROUBLE
Arsene Wenger had expressed concern that his Arsenal team had never practiced, much less played, on an artificial surface like the one at Swedish side Ostersund. He neednt have worried.
Arsenal had little trouble easing to a 3-0 win thanks to an early strike by Nacho Monreal and passes by Henrikh Mkhitaryan that led to two more goals. Monreal scored after 13 minutes when he pounced after a shot by Alex Iwobi was saved by goalkeeper Aly Keita.
Mkhitaryan then laid on the third goal for Mesut Ozil in the 58th minute before Arsenal goalkeeper David Ospina saved a stoppage-time penalty by Tom Pettersson.
"People wondered why we didnt practice (on the pitch) before but the warm-up is good to adapt to the speed of the ball, for technical ability and the accuracy of the passing," said Wenger.
"We adapted very well because were at a good technical level. They were very nervous at the start and we took advantage of it." Arsenal was without injured striker Alexandre Lacazette while Aubameyang is ineligible to play in the competition.
Arsenal is sixth in the English Premier League, eight points behind Chelsea, which holds the fourth and last qualifying berth.
ATLETICO STARTS STRONG
Atletico Madrid overcame an early deficit in Denmark and strolled to a 4-1 win over Copenhagen.
After Viktor Fischers opener, Atletico responded with goals by Saul Niguez, Kevin Gameiro, Antoine Griezmann and substitute Vitolo.
Atletico has reached two Champions League finals since winning the Europa League in 2012. It returned to the continents second-tier competition after a disappointing group phase in this seasons Champions League.
Napoli is staring at an exit after falling 3-1 at home to Leipzig.
Substiute Adam Ounas gave Napoli the lead in the 52nd minute but Leipzig fought back with a double by Timo Werner and another goal by Bruma. Leipzig is a distant second to Bayern Munich in the Bundesliga.
OTHER GAMES
A hat-trick by Manuel Fernandes led Lokomotiv Moscow to a 3-2 comeback victory at Nice, which had gone 2-0 ahead with a double from Mario Balotelli.
Athletic Bilbao was lifted by two goals from 37-year-old striker Artiz Aduriz in a 3-1 win at Spartak Moscow, while AC Milan triumphed 3-0 at Bulgarias Ludogorets.
Real Sociedad drew 2-2 with Salzburg, Sporting Lisbon won 3-1 at Astana and Marseille defeated Braga 3-0.
Greek police detained 18 people, believed to be supporters of Dynamo Kiev, for questioning after a bar in Athens was damaged ahead of the Ukrainian teams 1-1 draw against AEK.
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