The French striker opened the scoring by outjumping Danny Higginbotham after a fine cross from Nadir Belhadj.
Libyan Islamist commander Abdel Hakim Belhadj has resigned his military post in a bid to enter politics.
Mr Belhadj told the BBC he is not asking for money, he only wants a formal apology.
Algeria totally lost their discipline and saw Nadir Belhadj and keeper Fawzi Chaouchi also dismissed late on.
Whether their assiduousness went too far in the case of Mr Belhadj is for Sir Peter's inquiry to determine.
Mr Belhadj, a key brigade leader in the 2011 toppling of Col Gaddafi, plans to run in elections next month.
Mr Belhadj was imprisoned in Libya following a secret rendition he claims the CIA carried out from Bangkok in 2004.
Algeria's frustration then told when Belhadj was given a straight red card for a two-footed lunge on Ahmed Al Muhammadi.
In came left-back Nadir Belhadj for his first start, and winger John Utaka was included after shaking off a knee problem.
Mr Belhadj is currently taking legal action against the UK authorities, alleging they were complicit in his 2004 rendition to Libya.
Once Qaddafi was overthrown, Chris Stevens was appointed as the ambassador to the new Libya run by Belhadj and his friends.
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Two former Libyan dissidents, Sami al-Saadi and Abdul Hakim Belhadj, allege that the UK was involved in their kidnap and rendition.
Although the cases of Baha Mousa and Mr Belhadj are being aired at the same time, they are in fact very different.
Only a linesman's flag denied the visitors the opener, Danny Webber flicking Nadir Belhadj's cross in at the near post from an offside position.
One of the team's more established players, Nadir Belhadj, was among the most frustrated, as he attempted to link up play and pass the ball around.
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Although Nadir Belhadj pulled a goal back for the home side, midfielder Alex Song nodded in a fourth with 10 minutes left from Nasri's right-wing cross.
Meanwhile, Libyan political analyst Sami Khashkhousha told the BBC he believed Mr Belhadj's chances in politics were remote, saying liberal parties are likely to be more successful.
Belgian defender Vanden Borre tried to make amends with a decent shot which was well saved by Edwin Van der Sar, who also smothered an effort from Nadir Belhadj.
Mr Belhadj told the BBC his message to other rebels and militiamen is to rebuild a new Libya, and that they need to join the state's security or civil institutions to do so.
Earlier this year Mr Belhadj alleged that British ex-foreign minister Jack Straw and the UK government's various spy agencies were complicit in his rendition to Libya, where he says he and his wife were tortured.
Some are wary of ex-military personalities joining politics altogether, she says, but others hope Mr Belhadj's move will encourage other rebel strongmen to abandon their guns and join Libya's political process to rebuild the country.
On 18 April it was revealed that a Libyan military commander, Abdel Hakim Belhadj, was taking legal action against former foreign secretary Jack Straw for allegedly agreeing to his rendition to Gaddafi's Libya via British territory in 2004.
Letters from MI6 officials to members of the former Libyan regime, which were discovered in a Tripoli building in the aftermath of last month's rebel takeover of the city, are said to lend credence to Mr Belhadj's allegations.
But a minute later, Zidan more than made up for it when he picked up the ball at the edge of the box and danced inside Belhadj to slam home beautifully into the top corner for a splendid second goal.
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