Dowell’s lovely header settled the context in the Black Country as the Blades produced a sound response following victories for Leeds and Norwich City earlier in the day.
Accomplished in the first half, the Blades then kept their discipline in a scrappy second period and ensured that there was no repeat of the drama in their recent away fixture at nearby Aston Villa.
It was a professional performance from the visitors, who look to possess the stamina associated with top-two contenders with Chris Wilder’s side having now been beaten just once in 12 league matches.
The Blades made three changes to the side who trounced Reading last weekend, with captain Billy Sharp, Dowell and David McGoldrick restored to the starting line-up.
It was Dowell who produced the telling moment in the first half to fire United in front and crown an accomplished half against opponents who showcased plenty of evidence of just why they have laboured on home soil of late.
A probing break on 14 minutes saw down the right saw Kieron Freeman supply Martin Cranie, with the utility man doing superbly to keep the ball in play and stretch out a leg and guide it into the danger area with the lurking Dowell netting with a beautifully placed header.
It was just reward for an accomplished first half in which the Blades possessed far more conviction and aplomb than Albion, with it easy to see why they were without a league win at the Hawthorns since Boxing Day.
The Blades went close to doubling their tally on 19 minutes when Sam Johnstone - who excelled for Aston Villa at Bramall Lane last season - made a fine one-handed save to turn away Marvin Johnson’s low curler following a clever touch from Dowell.
The Blades loanee posed no end of problems for the flaky home defence in the first period, with Albion also looking decidedly one-paced in central midfield and not resembling automatic promotion contenders.
Despite producing some dangerous moments on the break, Albion did not overly trouble the Blades rearguard, with Dean Henderson forced to make just one half-decent save.
It came when Matt Phillips’ outswinging corner found the head of Craig Dawson, whose header was gathered comfortably enough by the Blades keeper.
Jay Rodriguez failed to get a telling connection to a fine early cross from Mason Holgate, while Dwight Gayle - booed by the away contingent following his return from a two-match ban - could not guide Rekeem Harper’s downward’s shot towards goal following home pressure, but it was United’s half.
The Blades were forced into a change at the interval with John Egan being replaced by Richard Stearman.
On the restart, Albion continued to flatter to deceive and they were fortunate to escape a red card on fifty minutes when referee Oliver Langford failed to spot a high challenge from Kieran Gibbs on Kieran Freeman.
Eventually, some semblance of home pressure did arrive, but the Blades were still comfortable enough at the back, although they were indebted to a key clearance from Enda Stevens to deny Jay Rodriguez.
Chances were at a premium with the Blades afforded one dangerous moment when the unmarked Gayle failed to connect in front of goal following a pinpoint Gibbs cross from the left.
At the other end, a half-chance saw Sharp glance a header wide following Freeman’s centre, while substitute Gary Madine shot straight at Johnstone.
Albion had the ball in the net on 84 minutes, but it was rightly ruled out for a handball after Rodriguez as he rose in the box following Holgate’s centre from the right flank.
Henderson did well in stoppage time to race out and deny Gayle.
West Brom: Johnstone; Holgate, Hegazi (Adarabioyo 65), Dawson, Gibbs; Harper, Barry, Livermore (Edwards 87), Phillips (Montero 65); Gayle, Rodriguez. Substitutes unused: Bond, Bartley, Johansen, Field.
Sheffield United: Henderson; Cranie (Basham 75), Egan (Stearman 65), Stevens; Freeman, Norwood, Fleck, Dowell, Johnson; Sharp, McGoldrick (Madine 64). Substitutes unused: Moore, Hogan, Coutts, Duffy.
Referee: O Langford (West Midlands).
Attendance: 24,928 (2,673 Sheffield United supporters).