The Valencia forward subdued a 25,000 strong crowd in Doha with simple strikes in the 39th and 59th minutes as Brazil strolled to victory against a limited, but willing Egyptian side playing for the first time under former United States coach Bob Bradley.
Hassan, 36, came on as 73rd minute substitute, putting him level with Saudi Arabia goalkeeper Mohamed Al Deayea, who last played in 2006.
Egypt initially did little to threaten Diego Alves' goal and only a desperate goalline clearance by Ahmed Hegazi prevented Oliviera netting his second immediately after the re-start.
The match then descended into a midfield stalemate until Lucas won a free-kick on the left-flank level with Egypt's penalty area.
Bruno Cesar swung the ball in and Egyptian keeper Ahmed el-Shanawi could only palm Fernando Luis Roza's header into the path of Oliveira and the 27-year-old made no mistake from three metres.
Egypt's response was immediate. Attacking the end where their most vocal supporters were gathered, Salah played in Ahmed Elmohamady, on the left and he cut inside and hit a rising shot that Alves could only parry away for a corner.
Hulk could have added a third for Brazil on 83 minutes, the forward blazing over following a intricate passing move that was started by a sliding tackle from Lucas, the game's outstanding performer as he controlled midfield.
Late substitute Dudu gave a lively cameo, spurning two chances to extend Brazil's lead.
