The Aces (20-13) gave the Chicago Sky (19-13) a chance to overtake them for the No. 4 seed in the playoffs and a first-round bye. Las Vegas holds the tiebreaker over Chicago and can still wrap up the fourth seed with a win in the season finale Sunday at Phoenix.
A'ja Wilson scored 19 points for Las Vegas.
Wilson made a pair of free throws to pull the Aces to 76-74 with 23 seconds left, but Alex Bentley answered with a pair of free throws four seconds later and Las Vegas missed its final three shots.
Atlanta avoided securing the worst record in the WNBA this season, although that distinction still looms with either a loss to the New York Liberty in the season finale or a Liberty victory over Indiana on Friday.