Jadon Sancho fed Paco Alcacer for Dortmund's opener just after the break before clinching the victory and his side's first trophy since 2017 with a clinical finish.
Ozil quit international football last month amid the furore over his meeting and photo opportunity in May with Turkish president Recep Tayyip Erdogan, which raised questions about Ozil's loyalty to Germany.
Germany's lost to Mexico has thrown their World Cup defence in disarray.
Mexico created the first upset of the 2018 FIFA World Cup, overcoming defending champions Germany 1-0 in a frenetic Group F game at the Luzhniki Stadium on Sunday.
Joachim Loew omitted Manchester City striker Leroy Sane from his 23-player list despite a strong season with the Premier League champions.
Germany are now winless in their last five games since suffering back-to-back defeats after losing 0-1 to Brazil in Berlin last March.
World Cup holders Germany appear to have been given a fairly kind draw in Group F alongside Mexico, Sweden and South Korea as they aim to become the first country to successfully defend the trophy since Brazil in 1962.
Manuel Neuer will return to international action in World Cup warm-up match against Austria after more than eight months
Neuer, Germany's captain and goalkeeper, has not played since September and still has to prove his fitness at a fortnight-long training camp.
Germany coach Joachim Loew said he wanted to increase the prospects of young players, as die Manschafft's opening 2018 World Cup qualifier match against Norway in Oslo on September 4
Bayern Munich goalkeeper Manuel Neuer was on Thursday named the new captain of world champions Germany following Bastian Schweinsteiger's international retirement
Manuel Neuer has worn the captain's armband in a total of 14 internationals, and had also led Germany in five matches of Euro 2016
Manuel Neuer, who has conceded just one goal in Euro 2016, will be aiming to keep Antoine Griezmann, the top scorer at bay in the semi-final
Manuel Neuer, who is a virtual wall in front of goal is once again turning out to be a key player in Germany's quest of another major title. Just how big a factor is the Neuer factor?
Germany are through to the semifinals of Euro 2016 after a nail-biting win over Italy in the last eight. Germany prevailed 6-5 in a penalty shootout after the game finished 1-1 in regulation time. Get highlights of GER vs ITA here.
Joachim Loew's Germany insist they have no 'Italy trauma' as they look to beat the Azzurri at the ninth attempt on a big stage and throw off their Italian shackles
Germany, coached by Joachim Loew, progressed to the last 16 as winners of Group C, beating Ukraine and Northern Ireland, drawing with Poland and all without conceding a single goal.
Defender Shkodran Mustafi powered home the opener from Toni Kroos's free-kick after just 19 minutes of Sunday's Euro 2016 encounter and Bastian Schweinsteiger wrapped up the win for Germany in added time, moments after coming off the bench against Ukraine