Their pairing on Thursday made for a tableau impossible to imagine eight years ago when Mr. Obama was engaged in a battle with Mrs. Clinton for the Democratic nomination. But on Thursday in the center of a large arena, the first black first lady stood beside the former first lady who is seeking to break yet another historic barrier by becoming the first woman to be president, making common cause against Mr. Trump.

“It doesn’t get any better than being here with our most amazing first lady,” Mrs. Clinton told a packed hall here at Wake Forest University. Comparing Mrs. Obama to the author and poet Maya Angelou, Mrs. Clinton called the first lady “another woman whose voice we need now more than ever.”

“I wish I didn’t have to say this, but indeed, dignity and respect for women and girls is also on the ballot in this election,” Mrs. Clinton said, “and I want to thank our first lady for her eloquent, powerful defense of that basic value.”

Starting with a prime-time speech at the Democratic National Convention in July, Mrs. Obama — who has done little to hide her distaste for campaign politics — has become an invaluable asset for Mrs. Clinton. Her phrase denouncing the personal attacks of the campaign — “When they go low, we go high” — has turned into a favorite call-and-response that her audiences recite rapturously, similar to Mr. Obama’s “Fired up? Ready to go!” chant in his 2008 campaign.

“Casting our vote is the ultimate way that we go high when they go low,” Mrs. Obama said again on Thursday.

As the first lady has become a louder voice in the campaign, Mr. Trump has tried to call attention to the friction that once existed between Mrs. Obama and Mrs. Clinton. One of his tactics has been to resurrect an eight-year-old comment the first lady made during the 2008 primaries.

“Our view was that if you can’t run your own house,” Mrs. Obama said at the time, “you certainly can’t run the White House.” The remark was interpreted by some as a veiled dig at Mrs. Clinton that was meant to refer to Bill Clinton’s sexual indiscretions. The Obamas insisted then that it was a comment about their own family, seeking to explain how they balanced politics with the raising of their daughters.