TOKYO — For a moment they each hovered over the final hurdle, suspended in the air, armed with the painful knowledge of what the other woman again would force her to summon. Daliliah Muhammad’s right foot hit the track first. Three lanes to the left, Sydney McLaughlin landed next, and once more, she would have to chase down her beloved rival.

For two years, McLaughlin and Muhammad had pushed one another to rearrange what it is possible in the women’s 400-meters hurdles. McLauglin recently had seized the world record from Muhammad, but for at least another 40 meters, Muhammad still owned the Olympic gold medal. McLaughlin wanted it more than anything, and she would have to take it the hard way.

Wednesday morning at National Stadium, Muhammad ran the 400-meter hurdles in a time that would have beat any other woman on any other prior day. But McLaughlin caught her and passed her on the final sprint. She lunged over the line in 51.46 seconds and lowered her own world record by .44 seconds. Muhammad crossed in 51.58 seconds to defeat bronze medalist Femke Bol of the Netherlands, who at 52.03 seconds become the third-fastest woman ever in the event.