A early headed goal from Shkodran Mustafi set the Germans on their way before substitute Bastian Schweinsteiger sealed the win in stoppage time with a sweetly struck half-volley.

Victory puts Joachim Löw's side top of Group C on goal difference with Poland second following their 1-0 victory over Northern Ireland earlier in the day.

Next up for Germany on Thursday (June 16) is Poland, who beat them 2-0 in qualifying for Euro 2016, while Ukraine face Northern Ireland. 

Standing in for the injured Mats Hummels, 24-year-old Mustafi broke the deadlock in the 19th minute after powerfully heading Toni Kroos' free-kick past Andriy Pyatov for his first international goal.

Ukraine did cause Germany a scare shortly before half-time as Yevhen Konoplyanka forced Jerome Boateng into an acrobatic clearance off the line in the 37th minute. 

Moments later, Mykhaylo Fomenko's team had a goal ruled out with Artem Fedetskyi offside in the build-up.

Germany regained control after the break as they went in search of a potentially decisive second goal and a 30-yard strike from Kroos brushed the angle of the goal.

Another shaky moment at the back came three minutes from time when Mustafi's back-header went over Neuer, who had to shepherd the ball away from danger under pressure from Ukraine substitute Yevhen Seleznyov.

Any lingering doubts about whether Germany would hold on for all three points were put to bed when Manchester United midfielder Schweinsteiger converted Mesut Özil’s cross three minutes into stoppage time.

In Group C’s earlier game, Northern Ireland’s first match at a European Championship finals ended in defeat as Arkadiusz Milik scored the only goal of the game at the Allianz Riviera stadium in Nice.

The striker, who plays his club football for Dutch giants Ajax, slotted home a low shot in the 51st minute after being picked out by team-mate Jakub Blaszczykowski.

Poland were good value for the three points, the first time they have won an opening match at a European Championship finals.

Northern Ireland's loss was their first in 13 games and they must now get back on track against Ukraine. 

There was also a victory today for Croatia in the opening match of Group D as Luka Modric's superb long-range volley proved enough to beat Turkey at the Parc des Princes in Paris.

The Real Madrid midfielder struck four minutes before half-time and his team dominated after the break, creating several opportunities to increase their advantage. 

Darijo Srna and Ivan Perisic hit the woodwork, while Turkey keeper Volkan Babacan made a number of good saves.

Defending champions Spain are due to begin their Group D campaign tomorrow against Czech Republic after which Group E takes centre stage with matches between the Republic of Ireland and Sweden, and Italy and Belgium.