Hillary Clinton received a surge of support after the Democratic National Convention, according to a new national poll that showed her opening a lead against Donald J. Trump with fewer than 100 days to go before the presidential election.

The CBS News survey released on Monday shows 46 percent of registered voters backing Mrs. Clinton and 39 percent supporting Mr. Trump, the Republican nominee. That represents a four-percentage-point bounce for Mrs. Clinton, who was deadlocked with Mr. Trump after the Republican convention, which gave Mr. Trump a two-point increase.

When Gary Johnson, the Libertarian Party’s nominee, is added to the mix he receives 10 percent of the vote and Mrs. Clinton holds a five-point lead.

The CBS poll found that the Democratic convention improved Mrs. Clinton’s favorability rating and her standing with female voters, a group that was already strongly in her corner. She continues to trail Mr. Trump with men and white voters who do not have college degrees.