Williams netted the opener after 45 minutes on Saturday before Emnes notched his sixth league goal of the season seven minutes after the interval to ensure Boro returned to winning ways following their first defeat of the season in midweek, a 2-0 away defeat to Nottingham Forest.
The three points gave Boro their first win in six league matches and lifts Tony Mowbray's side up to second in the Championship table.
Derby, who hit the bar three times in the second half, have slipped down to sixth and are without a win in five league matches.
Visiting manager Nigel Clough gave striker Mason Bennett, aged just 15 years and 99 days, his debut alongside Theo Robinson up front, with Tomasz Cywka, who scored in the midweek draw with Reading, dropping to the bench.
England Under-16 international Bennett has netted regularly for the Rams' Under 18s this season and becomes the youngest player in Derby's history, replacing the previous record holder Lee Holmes.
The hosts had the opening chance of the match, but Julio Arca shot straight at Frankie Fielding from 20 yards.
The lively Bennett, a Shirebrook schoolboy, wasted his first opportunity, heading wide from Robinson's cross after seven minutes.
Williams headed straight at Fielding from six yards and at the other end, Robinson headed Ben Davies' free-kick wide from close range.
Boro almost opened the scoring after 32 minutes but Emnes' effort had to be bundled off the line by Lee Croft.
Scott McDonald began to run at the Derby defence but, after finding space, the Australian fired two shots in quick succession wide, while Fielding had to be at his best to turn away Tony McMahon's 18-yard effort.
Boro's pressure finally told when, on the stroke of half-time, Justin Hoyte's effort was turned in by Williams, who found the top corner from close range despite a push in the build-up.
Derby came back into the game and Robinson was unlucky not to level as Jason Steele pushed the striker's effort onto the post and away for a corner. From the resulting corner, Bennett was denied by the Middlesbrough goalkeeper, who tipped the youngster's effort over the bar.
However, Boro went up the other end and made Derby pay as Emnes headed in a second from Hoyte's cross.
McDonald was once again denied by Fielding, while Steele parried substitute Chris Maguire's effort to Bennett, who crashed the rebound against the crossbar.
Substitute Jamie Ward hit the bar with a 20-yard strike after 77 minutes, and saw his cross deflected onto the woodwork late on but the hosts held on.
