The 20-year-old striker, the younger brother of Manchester United and England striker Wayne Rooney, was making his first start and he capped an impressive display with a clinical strike from just outside the area in the 65th minute to seal a 2-1 victory.
Nice John: Rooney (left) celebrates his winner for the Red Bulls
Delirious fans chanted his name and sang he's the 'best Rooney ever'.
The Red Bulls will now face Chicago Fire in the quarter finals.
The major upset of the third round, when Major League Soccer clubs joined the annual Cup tournament, was Columbus Crew's 2-1 loss to Richmond Kickers. Matthew Delicate scored the winner for Richmond in the 85th minute, ousting the Crew in its first match back in the US Open Cup since losing the 2010 final to Seattle Sounders.
Watch the video (Rooney goal at 7.32)
Elsewhere, Mike Fucito scored once in each half as the two-time defending champion Sounders beat the USL Premier Development League club Kitsap Pumas 2-1 and will now face LA Galaxy in the quarter finals.
Omar Gonzalez and Mike Magee scored within seven-minutes late in the second half to give the Galaxy a 2-1 victory over the Los Angeles Blues.
Gonzalez equalised in the 75th minute with a header from Juninho's free kick and Magee fired in from 11 yards in the 81st to seal the comeback win.
At Rochester, Diego Chaves scored in the 37th minute to give the Chicago Fire a 1-0 win over Rochester Rhinos.
Sweet 16: Rooney marked his first start for Red Bulls with a goal
Real Salt Lake had a 2-0 victory over the Wilmington Hammerheads and will travel to play a quarter final against FC Dallas, which needed Milton Rodriguez' header four minutes into stoppage time to edge Orlando City 3-2.
Sporting Kansas City had a 3-0 victory over the semi-pro Chicago Fire PDL and will host the Richmond Kickers in the July 12 quarterfinals.
'We've done it before so it's nothing new to us,' Richmond coach Leigh Cowlishaw said of beating an MLS team in the Open Cup. 'The big thing is we've done it on the road.'
The Crew lost defender Danny O'Rourke to a red card in the 67th minute and the Kickers were able to take advantage as extra time loomed.
On the slide: Blues defender Mike Randolph, right, challenges Galaxy midfielder Paolo Cardozo
Second-half substitute Edson Elcock's long pass found Delicate on the left to score the winner.
Richmond had taken a 1-0 lead in the 20th minute via Nozomi Hiroyama's 18-yard shot and Cole Grossman had equalised for the crew 17 minutes later.
The Crew started with five rookies who have seen little of MLS play and paid the price with an early exit from the Open Cup - a competition that began in 1914 and is open to all teams at the pro and amateur levels in the United States.
'I'm disappointed,' Crew coach Robert Warzycha said. 'This is a group (of players) fighting for one of the starting positions. I'm so disappointed.'
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