Luke Varney’s first-half header saw Leeds condemn Bolton to their fourth successive defeat in the Sky Bet Championship.
Wanderers, who were named among the favourites for promotion at the start of the season, looked devoid of ideas in attack throughout the match.
United’s win also sees the Trotters still searching for their first three points of the campaign, while they remain level with Millwall at the bottom of the table.
Leeds opened the scoring for the first time this season in the seventh minute.
After Zat Knight cleared for a corner, Luke Murphy’s delivery saw Varney get across his man and head the ball into the back of the net at the near post.