The victory for Mrs Merkel's party will now give her a boost as she seeks a fourth term in general election in September.
While Schulz now holds no public office besides SPD chief and thus has no natural platform beyond the stump, Merkel'office provides her with the best stage to burnish her reputation as Germany's Stabilitätsanker (anchor of stability) in an unstable world.
After a blaze of publicity earlier this year, Schulz - who chose not to join the government when he returned to Germany in January - has struggled to maintain a high profile.
SPD deputy chief Ralf Stegner called it a "very dark day for the SPD" but said the game is not over.
A defeat for center-left governor Hannelore Kraft in Germany's North Rhine-Westphalia state would be a major blow for the Social Democrats after poor showings in two previous state elections.
If the talks break down, he could attempt to form a "grand coalition" with the Social Democrats - mirroring the national government in which the party are junior partners.
Mr Schulz himself had acknowledged the importance of Sunday's vote after casting his ballot in his hometown of Wuerselen. Ms. Kraft announced that she was stepping down as the Social Democrats' regional leader.
The CDU is hoping to mount a national campaign in September built around Merkel (photo), who has been in office since 2005, as a force of political stability and a steady hand on the global stage.
Projections for ARD and ZDF public television, based on partial counting, Sunday showed Merkel's Christian Democratic Union beating the Social Democrats by around 34.5 percent to 30.5 percent.
CIA forms special unit focused on North Korea threat
North Korea, in response, has increased its missile tests and even hinted at a new nuclear test in the coming weeks. The center will work closely with the entire US national security community, it added.
Christian Leye, the Left Party's top candidate in the state, noted that "the Schulz train derailed in North Rhine-Westphalia".
Kraft has ruled NRW since 2010 in a coalition with the environmentalists Greens, whose support among voters has more than halved to just over 6 percent, making it difficult for the SPD to muster a coalition, especially as their natural partners, the hard-left Die Linke, are also on 6 percent.
Mr Schulz's comments indicate how Britain's departure from the European Union could become a hostage to fortune in domestic rows across the continent. In the state's last election in 2012, the Social Democrats beat the CDU by 39.1 percent to 26.3 percent.
"We will do everything not only to help France but also to shape the European path with France", Merkel said in the city of Aachen near the border with Belgium.
The polls showed the Social Democrats (SPD) coming in second, garnering 31.2 percent of the vote in its stronghold state, down over 7 points from the last election in 2012.
She had urged voters to look at her government's economic record, noting that with 7.5% unemployment, the state fares worse than the national rate of 5.8%.
On Mr Jaeger's watch, Cologne also became the scene of mass sexual assaults by groups of mostly North African men on New Year's Eve of 2015-2016, inflaming the debate over the 890,000 asylum seekers Germany welcomed in 2015.
The AfD is now represented in 13 states across Germany.
Yesterday's result could now pave the way for the state's first ever coalition between the CDU and the SPD under the 56-year-old Laschet.