The 22-year-old volleyed the ball with an overhead bicycle-kick into the top right-hand corner of goalkeeper Felipe's net in the 78th minute to deny Flamengo the victory that would have put them level with Corinthians at the top of the standings.
"The ball came to me very quickly, I managed to be well positioned to score a beautiful goal [but] the important thing is to help the team get results," Damiao told reporters.
Corinthians have 37 points following a surprise 2-0 home defeat by modest Figueirense on Saturday with Flamengo on 35. Vasco da Gama and Sao Paulo are both a point further back.
Flamengo had lost their unbeaten record in a shock 4-1 home defeat by Atletico Paranaense on Thursday without the suspended Ronaldinho, but he returned on Sunday to put Flamengo ahead with a trademark free-kick in the 25th minute.
Inter, despite having Argentine midfielder Pablo Guinazu sent off for a second booking before half-time, equalised six minutes into the second half at their Beira-Rio stadium in Porto Alegre when defender Indio scored from Damiao's smart backheel.
Substitute Jael put Flamengo ahead again with his first touch on the hour before Damiao's equaliser for his 32nd goal of the year in club competitions, the best in Brazil this season.
Copa Brasil winners Vasco were held 1-1 at home by Brazilian champions Fluminense. Former Olympique Lyon midfielder Juninho put Vasco ahead with a first-half penalty but striker Rafael Moura equalised after the interval.
Sao Paulo drew 1-1 with local rivals Palmeiras, taking the lead with a lob by striker Dagoberto over goalkeeper Marcos from former Brazil forward Rivaldo's pass. Central defender Henrique equalised for Luis Felipe Scolari's team.
