England are joined in the last eight by champions France who beat Switzerland 3-1 thanks to two late goals from Thierry Henry. Swiss striker Johann Vonlanthen took over from Rooney as the youngest scorer in European Championship history with his first half effort.
England now face a mouth-watering game on Thursday against hosts Portugal who had sparked a night of wild celebrations by beating neighbours Spain 1-0 on Sunday. Group B winners France will take on surprise package Greece on Friday, also in Lisbon.
Rooney, 18, is Euro 2004's top scorer with four goals, leading his normally understated coach Sven-Goran Eriksson to draw comparisons with Brazil's maestro.
"I sometimes try not to say things but he is absolutely incredible," said Eriksson. "I don't remember anyone making such an impact on a tournament since Pele in the 1958 World Cup."
His comments are sure to provoke lively debate among fans in Lisbon's heaving bars - Pele was just 17 when he scored six goals in 1958, including two in the 5-2 final win over Sweden.
There is no doubt, however, that Rooney's display will have club owners around the world checking their bank balances to see if they can afford a player whose worth to his employers, Everton, goes up by millions every game he plays in Portugal.
England, who needed just a draw to qualify, had suffered a shock after five minutes when Nico Kovac pounced from close range to give Croatia the lead.
Rooney created England's equaliser for Paul Scholes after 40 minutes and then belted his side in front six minutes later with a ferocious right-foot shot.
Rooney galloped clear to make it 3-1 after 68 minutes and although Igor Tudor headed a second for a spirited Croatia side, Frank Lampard sealed victory late on.
England captain David Beckham, no stranger to the limelight, joined in the celebration of the Rooney phenomenon.
"When you see him perform, nothing fazes him," said Beckham. "It was a big game tonight. He has produced again and he deserves all the praise he gets."
ZIDANE GOAL
In Coimbra, Zinedine Zidane headed France into a 20th-minute lead with his third goal of the tournament but Vonlanthen, 18 years and four months old, rocked the holders six minutes later with a cool angled finish.
Henry sealed a quarter-final place with his first goals of the tournament in the 76th and 84th minutes.
"It's good news to learn (Henry) is scoring goals again," Zidane said. "We are happy, just like he certainly must be."
Vonlanthen was playing only because striker Alexander Frei was provisionally suspended after television footage showed him spitting at an England player last week in Coimbra.
Frei, who has denied spitting, was pulled out of the Swiss team just hours before the kickoff. UEFA then announced that he had been suspended for 15 days.
Italy's preparations for their Group C match against Bulgaria in Guimaraes on Tuesday were hit by an injury to striker Christian Vieri.
Vieri has a knee injury and did not take part in the full pre-match training session on Monday. Midfielders Simone Perrotta and Cristiano Zanetti are also at risk for the game.
Conspiracy theories are still clouding the build-up to the other Group C match between Denmark and Sweden in which a 2-2 draw or higher would eliminate Italy.
The Swedes once again laughed at suggestions of a fix, saying they would aim for a win in the 90 minutes.
"It will be a very tough game, we all know what's at stake," midfielder Fredrik Ljungberg said.
"If it got to 2-2, and that's a good result for both of us, we would still go for the third goal and try to win."
Sweden and Denmark have four points to Italy's two. If Italy beat Bulgaria, a win in Porto would send one of the Scandinavian teams into the quarter-finals with the Italians.
More from rediff