Nigerian international Yakubu scored his seventh goal of the season in the first half and Australian striker Mark Viduka put the result beyond doubt with a two-goal, five-minute burst after the break.
Boro are now well-placed to qualify for the knockout stage of the UEFA Cup and the only disappointment of the night was the attendance of just 12,953, especially after Saturday's display against United.
Middlesbrough should heed the warning and slash the admission prices for the next UEFA Cup tie at the Riverside Stadium.
Boro are enjoying a purple patch after an inconsistent start the to the season and this was their third win in three different competitions in eight days.
Gaizka Mendieta, who scored a spectacular opening goal against Manchester United, tried to repeat the act with an early long-range shot against Dnipro.
But at first Boro lacked the power of their performance against United and the slow build-up of European football tested the patience of some restless fans.
Middlesbrough, however, got the breakthrough after 36 minutes following a good move between Mendieta and Yakubu. The Spaniard provided the pass and Yakubu the incisive finish.
Viduka had been an anonymous figure in the first half on his recall to the side but he had the crowd cheering with his clinical finishing just after the interval.
The referee allowed Boro the advantage after a foul and the ball fell to Viduka who hit a powerful shot into the net.
And after James Morrison's shot had been parried Viduka was on hand to score his second goal.
The Ukrainian side lacked the striking power to test Mark Schwarzer. It was a comfortable win for Boro and the players must now be expecting a good run in the competition.