Going into the game, Phil Parkinson opted for a return to a 3-5-2 formation, with Reece Burke joining Beevers and Wheater at the back, Mark Little replacing the injured Stephen Darby, Josh Cullen and Will Buckley playing alongside Jem Karacan in midfield and Adam Armstrong partnering Gary Madine up front.
In dreadful weather conditions, Wanderers had the first chance of the game inside the first five minutes. Mark Little's cross fell to Antonee Robinson, whose shot was blocked by Blades debutant Cameron Carter-Vickers.
A Sheffield effort was blocked by David Wheater, before Wanderers would carve out a couple more chances.
First, on loan Chelsea goalkeeper Jamal Blackman was on hand to save Gary Madine's speculative effort from thirty-five yards, before Jem Karacan headed Josh Cullen's wide.
Half an hour into the game, Wanderers were dealt a blow as Will Buckley went off injured to be replaced by Filipe Morais, who was now playing in an unfamiliar central midfield role.
Just three minutes later, Wanderers found themselves a goal down. After failing to properly clear Paul Coutt's corner, the ball was bundled in by Cameron Carter-Vickers, after his first shot was initially blocked by Mark Beevers.
It could have been two shortly after. Carter-Vickers again found space in the box, only to see his shot well saved by Ben Alnwick.
Despite a more spirited (and equally frustrating) performance, Wanderers weren't able to find that equalising goal.
They did have chances in the second half. Madine saw a goalbound header hooked away off the line, whilst Morais had plenty of opportunities to fire in a great cross from a free kick, but Jamal Blackman was on hand to collect every delivery with relative ease.
Morais did go close with a direct free kick, but he couldn't repeat his heroics from Millwall away and his effort landed on the roof of the net.
After Gary Madine received an inevitable yellow card, Sheffield United had to chance to extend their lead in the final minutes. Fortunately for Wanderers, Lundstream beat Alnwick only to see his effort come back off the crossbar.
The fourth home defeat of the season leaves Wanderers rock bottom, with just two points from their opening seven games.
Meanwhile, Sheffield United climb up to 3rd in the Championship table.
Next up for Bolton is a trip to Portman Road to face Mick McCarthy's Ipswich Town.