Conquerors of Hibs thrashed at Riverside
The Ukrainian visitors, who defeated Hibs 5-1 in the qualifying round, held their own for 35 minutes at the Riverside Stadium before the breakthrough. But once Boro strikers Aiyegbeni Yakubu and Mark Viduka made their mark on the game, Dnipro were beaten and could have conceded more.
The win takes Boro three points clear at the top of Group D, although favourites AZ Alkmaar have played just one game, and a point in Holland later this month will ensure their progression.
"It was important to win," McClaren said. "I think we only need another point from the next two games, so that puts us in the driving seat.
"It was a very professional performance. Only Chelsea have scored more goals than us this season in the Premier League, and we have scored another three tonight and haven't conceded."
Asked if Boro could now be considered among the Barclays Premiership's entertainers following their 4-1 defeat of Manchester United at the weekend, McClaren replied: "We were fourth top scorers last season, we have strikers capable of scoring. We always look to score."
It took 36 minutes for Yakubu to break the deadlock with his seventh goal of the season and first in Europe. He exchanged passes with Gaizka Mendieta - impressive again after his brace against United - and drilled a low shot past keeper Artem Kusliy.
But it was a devastating double from Viduka within 11 minutes of the restart which cemented victory and edged Boro towards a second successive appearance in the knockout stages.
First the Australian capitalised on some woeful defending to blast a 25-yard piledriver into the top corner, and then after Kusliy had saved well from James Morrison, he guided the ball into the empty net to make it 3-0.
Only a post denied Viduka a hat-trick, but the margin of victory was handsome enough as Boro belatedly made their new 3-5-2 formation pay dividends once again.
Dnipro's caretaker boss Vadym Tischenko admitted his side had been well beaten.
"I am disappointed by the result, but the score speaks for itself," he said. "Middlesbrough proved much stronger tonight."