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.
Many fans missed the start of a match, held to raise money for famine victims in Somalia, as gridlocked traffic outside the Rayyan Stadium prompted some cars to drive down dirt tracks, dodging flag sellers, while others gave up and abandoned their cars by the roadside or central reservation, walking the last mile to the ground.
Oliveira broke the deadlock as half-time neared, scoring with a simple tap-in after strike partner Hulk drilled in a low cross from the right byline.
Bradley replaced playmaker Mohamed Zidan with Ibrahim Salah for the second half and the Zamalek midfielder shone with some important interceptions and intelligent passes.
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.
That came to nothing and Brazil broke away, Oliveira missing a glorious chance to complete his hat-trick when he dragged a low cross-shot wide of the left post.
Hassan earned ecstatic whistling when he came on and nearly marked the milestone with a goal, his bouncing shot saved by Alves diving to his right.
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.
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