The Dynamo Kiev striker was picked out in the penalty area by Yevhen Konoplyanka before curling the ball into the top corner of the net.
However, Ukraine rode their luck 10 minutes from the end when Robert Lewandowski, who had a shot cleared off the line earlier, headed over from close range.
Mesut Özil got on the scoresheet as Germany confirmed their place in Brazil next year with a 3-0 victory over managerless Republic of Ireland in Cologne.
The Arsenal midfielder struck two minutes into stoppage time at the Rhein Energie Stadium after Sami Khedira and André Schürrle had scored either side of the break to finally kill off caretaker manager Noel King’s stubborn and much-changed Irish side, who hit the bar through Ciaran Clark at 1-0.
Özil’s late contribution was harsh on Republic goalkeeper David Forde, who had to pull off a string of fine saves, the best of them from Schürrle and Thomas Müller.
Wales looked to have earned some breathing space for under-pressure manager Chris Coleman as they moved off the bottom of Group A with a 1-0 victory over Macedonia in Cardiff.
The Welsh, missing 11 players from Coleman’s initial squad selection, ground out a first win in five games thanks to Simon Church’s close-range finish in the 67th minute, before the otherwise excellent Aaron Ramsey failed to convert a penalty.
Goran Pandev and Nikolce Noveski spurned two excellent chances for the visitors, but they could not find an equaliser and deny Craig Bellamy victory in his final home game in a red shirt.
Belgium reached their first World Cup finals since 2002 after on-loan Chelsea striker Romelu Lukaku scored two superb individual first-half goals to earn a 2-1 victory in Croatia.
Lukaku, who was replacing Aston Villa’s injured Christian Benteke, struck in the 15th and 38th minutes in Zagreb.
For the first Steven Defour fed the striker and he raced clear of centre backs Vedran Corluka and Dejan Lovren before rounding keeper Stipe Pletikosa.
The second was even better, having chipped the ball over Lovren inside his own half, Lukaku galloped past midfielder Mateo Kovacic, rounded the advancing Pletikosa and walked the ball into an empty net.
Switzerland also booked their place in Brazil with a 2-0 win in Albania, Granit Xhaka and Michael Lang getting the goals for Ottmar Hitzfeld’s side.
Bosnia are on the brink of their first World Cup finals, Manchester City’s Edin Dzeko scoring twice in a 4-1 home victory over Liechtenstein that means a win in Lithuania on Tuesday will secure qualification.
Robin van Persie became the Netherlands’ all-time top scorer when the Manchester United striker got a hat-trick in the 8-1 thrashing of Hungary in Amsterdam.
Van Persie now has 41 international goals, one more than Patrick Kluivert.
Nicklas Bendtner struck twice for Denmark but his goals were not enough to beat already-qualified Italy, who snatched a point from a 2-2 draw with Alberto Aquilani’s injury-time equaliser.
Zlatan Ibrahimovic’s late winner secured a play-off place for Sweden as they beat Austria 2-1 in Stockholm, while Real Madrid’s Karim Benzema finally ended his long scoring drought for France in their 6-0 friendly win over Australia.
Source: The Independent