United boss Sir Alex Ferguson rested key players with Tuesday's Champions League semi-final second leg against Arsenal in mind and, surprisingly, Middlesbrough rarely forced United to increase their tempo.
Boro, who remain second from bottom in the table, were bereft of ideas and relied on hopeful high balls into the area, which centre-backs Nemanja Vidic and Jonny Evans coped with admirably.
The home side did have one clear chance when Marlon King played in Aliadiere but Foster was alert to make the save.
At the other end, United's front pairing of Dimitar Berbatov and Federico Macheda were largely ineffective in a 4-4-2 formation.
First goal was important - Phelan
So when United scored, it was no surprise it came from the boot of the PFA Player of the Year, who is as desperate for his 11th league title as some of his team-mates are for their first.
Rooney found Vidic, who had been forward for a set-piece, who in turn laid the ball to Giggs. The 35-year-old Welshman steadied himself before placing his low effort wide of Jones' left from the edge of the area.
His veteran partner in the middle, Paul Scholes, 34, should have tested Jones after the break, but uncharacteristically failed to find the target with both of his long-range efforts.
Luckily for Scholes, United are not short of sharp-shooters. Their second came after a sublime move that saw Giggs and Macheda play a one-two before the fabulous Rooney threaded the ball to Park, who powered in a low drive.
It was the highlight of the match and underlined that gulf in quality between the two squads.
Southgate satisfied by Boro effort
Manager Gareth Southgate brought on £13m striker Afonso Alves and Didier Digard, but neither could ignite a Boro side flattened by United's double strike.
Southgate's side have three fixtures remaining to save their season, and are three points behind fourth-from-bottom Hull, who play at Aston Villa on Monday.
They now travel to fellow strugglers Newcastle a week on Monday, 11 May, in what promises to be a tension-filled clash, knowing they will have to improve tenfold in their remaining three games if they want to stay in the division.
Middlesbrough manager Gareth Southgate: "We've gone into the last two games against teams in the Champions League semi-finals and were looking for a miracle. To have a chance you need to take the lead.
"But we did get stuck into them early on but it is very tough mentally when you fall behind because they are so good defensively.
"The second goal killed the game but I have to give credit to my players because they never gave up.
"We have got to put this game behind us and start preparing for our next match against Newcastle, which is a huge game for both sides."
Manchester United boss Sir Alex Ferguson: "It's a big step forward with only four games left now. I keep saying you whittle the games away until there are none left.
"It was a very good performance, they all worked their socks off and once we got a hold of the ball we always looked a danger.
"Once we got in front, that was the key to it because they're a young side, Middlesbrough."
Middlesbrough: Jones, McMahon (Digard 55), Wheater, Huth, Hoyte, O'Neil (Emnes 70), Sanli, Bates, Downing, King (Alves 55), Aliadiere. Subs Not Used: Turnbull, Arca, Adam Johnson, Grounds.
Man Utd: Foster, O'Shea, Vidic, Evans, Evra (Rafael Da Silva 78), Park (Nani 74), Scholes, Giggs, Rooney, Berbatov, Macheda (Tevez 55). Subs Not Used: Kuszczak, Ronaldo, Anderson, Gibson.
Goals: Giggs 25, Park 51.
Ref: Mark Halsey (Lancashire)
BBC Sport Player Rater man of the match: Manchester United's Ryan Giggs (8.16 on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.