Germany beat Ukraine 2-0 while Poland secured a 1-0 victory over Northern Ireland.
The opening round of Euro 2016's Group C matches ended with victories for both Germany and Poland on Sunday.
Germany's stand-in centre back Shkodran Mustafi headed in his first goal and Bastian Schweinsteiger scored in stoppage time as the world champions survived several scares to beat Ukraine 2-0 in their opening match on Sunday.
Shkodran Mustafi is a top-class defender already.— Pellumb Mjeku (@ThisisPllumey) June 12, 2016
Mustafi, who started in the absence of regular centre-back Mats Hummels, rifled home a header 19 minutes into the game to give Germany the lead, which was not extended until Schweinsteiger, a 90th-minute substitute, scored from close range.
Schweinsteiger's goal which secured Germany's victory was also his first international goal since 2011.
That pass from Ozil & finish from Bastian Schweinsteiger— Noluthando Kampini (@Rose_Bud_Doll) June 13, 2016
Germany dominated possession, but also relied on three top saves from keeper Manuel Neuer and a goal-line clearance by Jerome Boateng to come out on top.
The result extended Germany's unbeaten run against Ukraine to six matches and maintained their record of never having lost their opening match in a European Championship.
Germany will play joint group leader Poland at the Stade de France on Thursday as Ukraine takes on Northern Ireland in Lyon.
Regarding the German victory, Ukraine coach Mykhailo Fomenko said Ukraine "just couldn't manage it."
"Germany is a machine, full of ideal players."
But despite the victory over Ukraine, Germany's coach Joachim Loew stated that his team would need to work hard in order to suppress the attacking threat of Poland when the two sides meet on Thursday.
"The game is really important for the future of the group. I think we will really have to put in some work.
"Poland are in any case a strong team. We've played them twice and of course we lost once. With Robert Lewandowski, they are strong in attack. Like Ukraine a little, they have dangerous players going forward."
Poland vs Northern Ireland
Poland's second-half winner from 22-year-old Arkadiusz Milik steered his team to a 1-0 victory ending Northern Ireland's first appearance at a major finals for 30 years in disappointment.
Milik's goal made him Poland's youngest goalscorer at Euro Championship.
Making their debut in the competition, the Irish were unable to cope with an attacking Polish outfit that dominated most of the opening match.
Despite a late rally from the industrious Irish, Poland never looked likely to lose although coach Adam Nawalka said they had to adapt for the abrasive style of their opponents.
"I have to praise the players for their commitment. Northern Ireland are known for their physical football so we had to adjust and offer the same in order to demonstrate our skills.
"The next matches will show that we can be even better and go further."