Manchester United 3 Middlesbrough 0
The teenage striker added two further spectacular strikes to his ever-growing repertoire of goals, with his latest efforts as good as any he has scored in his career.
Rooney netted his 10th and 11th goals of the season after defender turned midfielder player John O'Shea had broken the deadlock early in the tie.
Sir Alex Ferguson's former right-hand man Steve McClaren, whose side had lost only once in four return visits since he became Boro boss in 2001, had no complaints as his team were well beaten.
United had victory secured midway through the second half which enabled Ferguson to substitute Ryan Giggs, Cristiano Ronaldo and Gabriel Heinze with Tuesday's important Premiership match with Arsenal a little over 72 hours away.
The United manager was highly satisfied with his side's display, saying: "All you can do is win, and we did so convincingly. I'm absolutely delighted - it was a good all-round team performance, bearing in mind I rested Paul Scholes, while Roy Keane was suspended.
"We were energetic and lively and made it a quick game, something we intended, as Boro have a good record here and we didn't want them to sit back and settle.
"We started brightly and aggressively and got a goal early in the game, which is unusual for us."
Ferguson unsurprisingly singled out Rooney for praise, adding: "He scored two fantastic goals, and the boy is a special talent.
"But I was also pleased with the players I brought in, and they will have relished the opportunity to play in the first team. They didn't let me down."
McClaren also enthused about Rooney's performance, believing he will become an even better player. He explained: "Wayne's display confirms what I already knew about him. He was the big difference between the two teams.
"I could see he was special from the first training session I had with him with England.
"He has an excellent attitude and work rate and can only get better for England and United. Nothing phases him and he simply wants to play football.
"He gets better with every year, and if he keeps his feet on the ground, there is no telling what he may achieve by the time he is 22 or 23 years of age."
McClaren had no complaints about the defeat, but believes it might have been a different outcome if Boudewijn Zenden had not been denied by a great save from Roy Carroll in the opening half which would have made it 1-1.
Wes Brown came in to partner Rio Ferdinand in the centre of defence as Mikael Silvestre was rested, while in midfield there were call-ups for Phil Neville and O'Shea, who replaced Keane and Scholes.
Boro drafted in Colin Cooper to strengthen their defence, which had leaked four goals at Norwich, while James Morrison came into a five-man midfield at the expense of striker Joseph-Desire Job who was relegated to the bench.
United made an excellent start and had a penalty appeal for handball rejected, while Ronaldo headed over before they took a deserved tenth minute lead.
Quinton Fortune's cross from the left wasn't cleared and Ronaldo controlled the ball superbly on the edge of the penalty area to set up O'Shea, who fired high into the roof of the net from 12 yards. It was only his fourth goal in his 142nd first team appearance.
Boro came within a whisker of equalising in the 32nd minute with their first meaningful attack of the match after a rare lapse from Ferdinand.
Zenden found himself clean through on goal after taking a return pass from Jimmy Floyd Hasselbaink, but Carroll came to United's rescue, with an excellent block with his outstretched leg to deny the Dutchman.
Ronaldo then set up Rooney, who neatly side-stepped Cooper, only to see keeper Mark Schwarzer thwart him with a good block. Rooney featured prominently in a couple of attacking moves in the opening half, but was unable to find a route to goal.
Boro made a half-time substitution, bringing on Job to partner Hasselbaink in an effort to provide them with more attacking punch. Brazilian Doriva was the player to make way for him.
United should have doubled their lead when Ronaldo broke clear on the right and squared the ball too far ahead of Giggs as Schwarzer raced from his goal to clear the danger.
Boro were again indebted to their Aussie keeper in the 62nd minute when he made a brilliant save low to his right to keep out Ronaldo's goal-bound header which came from a Giggs cross and had goal stamped all over it.
Louis Saha replaced Giggs, who had another excellent match, midway through the second period, the switch again no doubt influenced by the imminence of the Arsenal match.
United scored their decisive second goal in the 67th minute, after Gary Neville played a wonderful ball over the Boro defence. Rooney ran through to lob Schwarzer, who had raced from his line and was caught in no-man's land.
Soon afterwards, Ferguson took off Ronaldo and Heinze as Liam Miller and Silvestre were given run-outs, and Rooney provided the icing on the cake with a stunning third goal in the 82nd minute.
Carroll's long clearance was headed on by Saha for Rooney to find the net with the sweetest of volleys over the head of Schwarzer from outside the penalty area.