Adams coolly steered home three minutes before the break to settle the contest as Rovers’ winless streak in all competitions stretched to a worrying six matches.
Rovers, whose manager Darren Ferguson was serving a one-game touchline ban, could have few complaints with a season which had been provided with momentum before Christmas now petering out - with the club’s supporters entitled to have one eye on developments at the foot of the table if their side’s alarm run of form continues.
While the immediate post-match concerns belonged to Ferguson, there was balm for his counterpart Nigel Adkins, whose side headed into the game with a poor run of one win in their previous six league outings
In a bid to cajole a winning formula, both managers made some significant changes, the most eye-catching of which came from Adkins.
One was admittedly enforced with a big pre-match blow seeing 14-goal top-scorer Billy Sharp miss out on lining up against his former club where he is so revered, with the Blades marksman sidelined with a slight foot injury.
His absence paved the way for a milestone first league start for Dominic Calvert-Lewin, back from a rewarding loan spell at League Two high-fliers Northampton Town, where he notched eight goals in 26 appearances.
Two other teenagers in Louis Reed and Adams were also promoted to the starting line-up, with Jamal Campbell-Ryce also returning to the side.
Ferguson made three key changes also with Andy Butler back in the side after a groin injury to line up against his old employers, with Nathan Tyson also a major returnee along with Cameron Stewart, with James Coppinger missing from the match-day squad along with Conor Grant, still sidelined with a rib injury.
It was the Blades, seeking to end a deflating run of results, who made the more accomplished start, twice going close to making the breakthrough.
First, Reed’s pass was not cut out by Luke McCullough and found its way to Jose Baxter, whose toe-poke was tipped over in the nick of time from Chris Neal, prefered in goal to the fit-again Thorsten Stuckmann.
Soon after, Rovers were afforded a graver scare with Neill Collins’ header hit the crossbar following Baxter’s cross.
Slowly but surely, the hosts - employing a 3-5-2 formation with Lynden Gooch in a deep-lying role, started to impose themselves on proceedings without carving out a clear-cut opportunity.
One moment of genuine alarm for the Blades saw Aaron Taylor-Sinclair neatly play in Cedric Evina down the left and his inviting cross flashed across the six-yard box, with no home player able to get a telling touch.
But it was the Blades who had the better of the opening half-hour, with another dangerous moment seeing Calvert-Lewin see a far-post header fly into the side-netting after John Brayford’s deep cross.
A mini flurry from Rovers then saw Collins block Williams’s shot before Adams’ lob was held by Neal after the youngster outmuscled Butler in pursuit of Reed’s probing pass.
A momentary lapse from the Blades defence soon afforded a half-chance for Williams, but his chip was easily held by Long, who was given plenty of protection for the vast majority of the half in which the visitors bossed the possession.
An encouraging first period was soon crowned by an opener from the visitors and on the balance of play, Rovers couldn’t have too many complaints.
Baxter’s delightful pass was latched onto by Adams, who cashed in on some hesistancy by Butler before poking the ball past the onrushing Neal with a cool low finish.
The hosts made an interval change, reverting to a back four with ex-Blades defender Craig Alcock coming on for Butler.
After a pretty low-key first period, the onus was very much on Rovers to show more assertion, but it was the Blades who had the first sniff of goal with Collins’s looping header held by Neal following Baxter’s floated cross.
A pertinent passage of home play saw Stewart’s powerful cross-shot parried at his near-post by Long, but it wasn’t the prelude to Rovers taking a stranglehold on proceedings, with the Blades looking fairly comfortable.
Out of nothing, Rovers manufactured their best moment of the game thus far a few minutes before the hour mark with Harry Middleton’s cross-shot flying across the face of goal, with the outstretched leg of Tyson agonisingly just failing to divert the ball home.
Play proceeded to become scrappy with Rovers looking devoid of quality in the final third and the Blades looking comfortable.
Neal then held a header from Edgar following Campbell-Ryce’s deep cross as the Blades scented a killer second goal.
That should have arrived on 72 minutes with a sweet move seeing Reed play in Adams, whose delicious dummy left McCullough totally flat-footed before he teed up the onrushing midfielder from point-blank range, but Neal made a key block.
The Blades proceeded to see out the game with few alarms to bag a precious three points.
Doncaster Rovers: Neal; McCullough, Butler (Alcock 45), Taylor-Sinclair; Stewart (Chaplow 77), Keegan, Middleton, Gooch (Mandeville 62), Evina; Williams, Tyson. Substitutes unused: Stuckmann, Lund, Lecygne, Davies.
Sheffield United: Long; Brayford, Edgar, Collins, McEveley; Campbell-Ryce (Flynn 75), Hammond, Reed (Basham 82), Calvert-Lewin (Woolford 85); Baxter, Adams. Substitutes unused: Howard, Coutts, Done, Sammon.
Referee: M Dean (Wirral).
Attendance: 10,168 (3,784 Sheffield United supporters).