Ukraine beat Slovenia 2-0, while Sweden took a 2-1 advantage in their first leg playoff against Denmark. The winners of both ties go through to the finals in France.
Sweden scored two quickfire goals either side of halftime to beat Denmark 2-1 in a Euro 2016 playoff first leg on Saturday.
Emil Forsberg netted the opener for the hosts and also won a 50th-minute penalty that Zlatan Ibrahimovic converted, before Nicolai Jorgensen snatched a late goal to leave the tie delicately balanced going into Tuesday's return match in Copenhagen.
Danish coach Morten Olsen believes his side can overturn the deficit next week.
"You have to be confident," Olsen told a news conference. "I think we have the players who can make the difference, it will be a different game."
Moment of silence
Both sides wore black armbands, and a moment's silence was held in memory of the 129 people who died in Friday's Paris attacks.
A similar tribute was paid at the other Euro 2016 first leg playoff of the evening, which saw Ukraine beat Slovenia 2-0.
Goals from Andriy Yarmolenko and Yevhen Seleznyov gave Ukraine the first-leg win ahead of Tuesday's repeat encounter.
"We played well and the result we've achieved is pretty pleasing but it's only half-time in the tie," Ukraine's manager Mikhail Fomenko said after the match. "I expect a very tough match at Maribor as Slovenia are a strong and well-organized team and now have nothing to lose," he added.
The winners of both ties go through to the finals in France.
mm/cmk (AFP, Reuters)