Four days after Tony Mowbray's three-year spell as Boro boss came to an end, his B#1million summer signing Adomah lit up the Riverside Stadium with a classy lob and a firm header in the first half.
An impressive haul of five goals in three games for the ex-Bristol City man was then consolidated by Sierra Leonean striker Kei Kamara and on-loan Daniel Ayala, who scored at the death to suppress a tame Doncaster revival.
It was a sixth league defeat of the season for Paul Dickov's men, who dominated possession but consistently fell prey to a starting XI specifically designed to inflict damage on the counter-attack.
Chairman Steve Gibson this week called time on Mowbray's tenure, just days after defeat to struggling Barnsley left his club within four points of the relegation places.
The poor return of only five league wins in 2013 and the thought of another miserable jostle for the best bottom-half finish had ultimately forced the ambitious owner's hand.
Friday night rivals Doncaster, having played a game less, shared 16th place with their hosts and the play-off places were 10 points away before kick-off.
Gibson had challenged Mowbray's long-serving assistant Venus to force his name onto the shortlist for interview and his successful audition took place in front of a bumper crowd of 21,882, with two players in particular helping him make an excellent first impression.
Only eight minutes had gone when Kamara caught Doncaster cold with a scooped through-ball into Adomah's path.
The Ghanaian winger raced forward and his first touch saw Ross Turnbull beaten by a sublime chip.
The Doncaster goalkeeper then produced a smart stop from the lively Mustapha Carayol as Boro pressed for the second goal.
Worsening rain would curtail the tempo until Kamara weaved his way into the box. He squared the ball to Marvin Emnes who teed up Carayol, but the winger's finish ended up in the south stand.
It did not matter, though, as Adomah made it 2-0 nine minutes before the break.
Richard Smallwood tried his luck from distance and, while his lobbed shot was on course to beat the backtracking Turnbull, Adomah made sure with a bullet header.
Doncaster almost forced their way back into the game before half-time, Mark Duffy's corner scooting through the Boro box only for Rob Jones to miss the easy tap-in.
Rovers' resurgence continued past the interval and Duffy was unlucky not to find a supporting team-mate after breaking into the box in the 55th minute.
Kamara ended any hopes of a comeback 10 minutes later. Grant Leadbitter's free-kick found him at the far post and while the finish was unceremonious, the Riverside crowd rejoiced.
Doncaster had been convincingly beaten, but Spanish defender Ayala needed to make sure.
Leadbitter provided the killer cross again in the 83rd minute and Turnbull threw his hands up in despair after the Norwich loanee nodded home with a minimum of fuss.