Republicans have rallied behind Donald Trump in the weeks since he effectively clinched his party’s presidential nomination, helping him narrow Democrat Hillary Clinton’s once double-digit lead to just 3 percentage points, a new Wall Street Journal/NBC News poll shows.

Mrs. Clinton leads the New York businessman, 46% to 43%, in a test matchup between the two likely nominees, the poll finds. That represents a much tighter margin than her 11-percentage-point lead in April and marks the first time in Journal/NBC News polling...