The Blades had a handful of chances to win the game, with visiting captain Lloyd Kelly hitting his own crossbar with a clearance before Morgan Gibbs-White was denied one-on-one by goalkeeper Mark Travers.
Then came the game’s flashpoint late on, when Gibbs-White was wiped out in the box by Nat Phillips. But somehow referee Dean Whitestone didn’t blow his whistle, and the game ended goalless.
The best chance of the game came in injury time when Filip Uremovic, who had earlier produced a stunning last-ditch tackle to stop Philip Billing, had the freedom of Bramall Lane to pick his spot right in front of goal, but somehow fired wide instead.
Here’s how we rated United’s players during the game…
While you're here, please consider taking out a subscription to our new discounted sports-only package. You'll find all the details HERE. Your support is much appreciated. Chris Holt, Football Editor
1. Wes Foderingham 6
Another game, another clean sheet. Protected well by the defence in front of him and any work he did was routine by his standards Photo: Isaac Parkin
2. George Baldock 6
Couldn't hide his frustration at the officials after he felt they missed the ball going out of play on his wing. Baldock stopped, Dembele - and the game - continued and United escaped. Photo: Simon Bellis
3. Filip Uremovic 7
Made his second start for the Blades after his debut against QPR and looked composed early on whenever Bournemouth attacked down their left. Superb last-ditch challenge on Billing stopped the Bournemouth man as he looked to break through on goal. Had a chance to win it at the death but couldn't take it - which would have capped the perfect game for the new boy Photo: Zac Goodwin
4. John Egan 7
Defensively solid as ever, apart from one hairy moment when there was a lack of communication between him and goalkeeper Foderingham and Solanke tried to take advantage Photo: Zac Goodwin