In plenty of space, the midfielder blasted his cross beyond a completely unmarked Emile Heskey.
Rodallega's arrival softens the blow of Emile Heskey's departure to Aston Villa earlier this month.
Emile Heskey was unmarked at the far post from a corner but headed wide from six yards.
But England had heroes all over the field, from the sound David Seaman to the tireless Emile Heskey.
Emile Heskey has been given the nod ahead of Jermain Defoe and will partner Wayne Rooney in attack.
Striker Emile Heskey scored a brace for the Reds as Bruno Cheyrou, Sami Hyypia and Salif Diao also scored.
From the restart, Darren Anderton delivered a deep cross from the right, but Jaaskelainen gathered comfortably despite Emile Heskey's challenge.
This time around, Bent has been given his opportunity because of injuries to regular squad members Emile Heskey and Theo Walcott.
John Carew has made a timely return to fitness, especially given the knock suffered by Emile Heskey on international duty last week.
Other selection issues for manager Fabio Capello include whether to keep faith with striker Emile Heskey or bring in Tottenham's Peter Crouch.
James Milner converted the subsequent penalty and a Steven Ngonzi own-goal and Gabriel Agbonlahor and Emile Heskey's strikes seemed to seal it.
Tottenham striker Crouch scored twice as he started in attack with Gabriel Agbonlahor because of injuries to Wayne Rooney and Emile Heskey.
Emile Heskey set England on their way at Wembley when he turned in Steven Gerrard's cross at the near post after seven minutes.
The visitors were rewarded for a strong start when Emile Heskey robbed Sebastien Bassong and squared for Marc Albrighton to slide in and convert.
After struggling to respond, the home side improved after the break and Emile Heskey levelled with a cross-shot within seconds of coming off the bench.
After losing Emile Heskey and Wilson Palacios in January, it seems likely that Antonio Valencia will follow them out of the JJB Stadium this summer.
Earlier, Jamie O'Hara and Didier Zokora dragged shots wide for Spurs, while Emile Heskey was denied by Heurelho Gomes and Amr Zaki headed just wide.
Even when Carlton Cole and Emile Heskey withdrew in the wake of Saturday's game, Capello still refused to draft in the fourth-highest scorer in England history.
The pace of Ashley Young and power and knowhow of Emile Heskey were now proving every bit as threatening as Keane's guile and Cole's direct running.
Birmingham striker Emile Heskey has been left out of the 22-man squad despite being picked for the World Cup qualifiers against Northern Ireland and Azerbaijan in March.
BBC: SPORT | Football | Internationals | Crouch nets England squad call-up
Steven Gerrard gave coach Fabio Capello the perfect start to this South African mission when he slid Emile Heskey's pass beyond Tim Howard after only four minutes.
The Swede is expected to pick his first-choice strike partnership of Liverpool's Michael Owen and Everton's Wayne Rooney with Emile Heskey and Alan Smith on the bench.
Scharner pounced on the hour mark to turn the ball in at the far post after Emile Heskey's close range effort was parried by Derby keeper Roy Carroll.
James Milner, Ashley Young and Gabriel Agbonlahor burst in behind defences brilliantly, feeding off the second ball provided them by the target man, Emile Heskey or John Carew.
Most of the visitors' early chances came from moves down either flank and the Eagles were fortunate to survive when Claude Davis beat Richard Dunne to Emile Heskey's knockdown.
Emile Heskey had proved a real handful, and he almost extended Wigan's lead with an acrobatic over-head kick after 50 minutes that brought an equally spectacular save from Paddy Kenny.
Ravaged by injuries to key players like captain Stiliyan Petrov and Emile Heskey, Houllier's side are on a dismal run, with just one win in their last 11 league games.
BBC: Gerard Houllier explains Liverpool remark to Villa fans
England's World Cup campaign was thrown into disarray when a challenge involving Emile Heskey led to Ferdinand injuring his knee ligaments at the end of England's first training session in Rustenburg.
BBC: Rio Ferdinand will not return to World Cup after injury
Aston Villa frontman Emile Heskey would appear to be Capello's first-choice striker to play alongside Rooney in attack, having started the last six matches for which he was fit and available.
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