Skipper Billy Sharp was the hero again, scoring in either half to secure victory, while Morgan Gibbs-White also made his long-awaited return from injury as a second-half substitute.
But there was an injury scare for the Blades when David McGoldrick, who was influential throughout, had to be helped off in the second half after picking up an unspecified knock.
The Blades are now level on points with the Baggies, who spanked them 4-0 at the Hawthorns earlier in the season. But Heckingbottom’s Blades have shown they are made of much sterner stuff.
This is how we rated the Blades’ players on an impressive evening at Bramall Lane…
1. Wes Foderingham 6
Relatively untroubled throughout the game, save for the odd routine save that he eats up for breakfast. Was confident and decisive coming off his line to punch balls away too
Photo: Andrew Yates
2. Jayden Bogle 6.5
Kept his place at right wing-back after his impressive displays of late, but couldn't hit those same heights in the first half. Improved in the second and tested Johnstone with a well-struck left-footed effort, which the England 'keeper did well to keep out with a strong hand
Photo: Isaac Parkin
3. Chris Basham 7.5
Early on on his 300th league appearance for United he cut inside, exchanged nice passes with McGoldrick and then had a go on his left foot. He couldn't trouble Johnstone, but it signalled United's intentions. Had a let off when he gave the ball away to Livermore, but Egan did well to bail him out
Photo: Simon Bellis
4. John Egan 7.5
Facing the difficult task of marking the awkward and strong Carroll, the former Newcastle man barely had a sniff all night
Photo: Mike Egerton