Midfielders Oleksiy Gai, Willian and Darijo Srna put the Ukrainians 3-0 up at half-time in one of 24 matches played with additional assistant referees (AAR) beside each goal to spot fouls and dives in the box.
Karel Geraerts pulled one back for the home side just past the hour before Konstantyn Kravchenko's goal wrapped up an emphatic Group J win for Shakhtar in the remodelled UEFA Cup.
If the experiment with AARs is successful they are likely to be introduced into the game at large within a season or two.
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Basel enjoyed a surprise 2-0 win over visiting AS Roma to spoil coach Claudio Ranieri's first European match since he replaced Luciano Spalletti two weeks ago after their poor start in Serie A.
Winger Carlitos capitalised on a defensive mix-up early in the Group E match and Federico Almerares struck three minutes from time to wrap up victory for the Swiss.
"It was an ugly defeat," former Juventus and Chelsea boss Ranieri told Mediaset television.
"We were not very solid and I saw too few touches of the ball. We have to try to be less beautiful but more concrete. The lads have to learn to react and concentrate for 90 minutes."
FLYING START
Galatasaray, the 2000 UEFA Cup winners, also got under way positively in Group F thanks to a 3-1 win over Panathinaikos in Athens, with the Turkish club's coach Frank Rijkaard getting the better of Henk Ten Cate, once his assistant at Barcelona.
Panathinaikos' city rivals AEK Athens went down heavily too, losing 4-0 at Everton in Group I.
Defenders Joseph Yobo and Sylvain Distin got the final touch to corners and Steven Pienaar drove home from 25 metres before Jo sealed the win for the English outfit with a simple finish.
Four times European champions Ajax were held to a goalless draw in Amsterdam by Romania's FC Timisoara in Group A.
Celtic, who have also been European champions, paid the price for sitting on the first-half lead Greek striker Georgios Samaras earned them at Hapoel Tel Aviv in Group C.
Serb midfielder Nemanja Vucicevic and forward Maaran Lala found the net in the last 15 minutes to earn the Israelis a 2-1 win after Samaras had to come off in the second half having hurt himself falling into one of the dugouts.
Hamburg SV's hopes of reaching the final at their home stadium in May were dented when they were thrashed 3-0 at Rapid Vienna in the other match in the group.
Athletic Bilbao thumped Austria Vienna 3-0 and last year's UEFA Cup finalists Werder Bremen won 3-2 at Nacional Madeira in Group L.
Roma's city rivals Lazio handed a
