Sardar Azmoun gave Iran the lead with a header in the 11th minute and Mehdi Taremi found the back of the net after receiving a neat pass from Ehsan Haji Safi in the 19th minute.
It was center-back Farouk Chafai who got Algeria back in the contest in the 56th minute, when he was picked out by a Mokhtar Benmoussa cross and made no mistake in sending a header home.
Iran had lost to Tunisia 1-0 on March 23 in Tunisia.
Team Melli has been drawn in Group B of the 2018 World Cup along with Spain, Morocco and Portugal.
Iran selected Tunisia and Algeria due to their games similarity with the Moroccan national squad.