As in last week's 4-1 win over Troyes, Les Gones had to come from behind after conceding a goal early in the second half, Cedric Barbosa scoring in the 55th minute.
But Bastos, who scored a spectacular second on Saturday, hammered home a free-kick to preserve Lyon's unbeaten start to the season.
Evian had the better of a quiet first half, but Ali M'Madi failed to hit the target after being picked out by Daniel Wass and Hugo Lloris saved well from Yannick Sagbo.
Bafetimbi Gomis had Lyon's best chance of the opening 45 minutes when he raced on to Jimmy Briand's through-ball but Bertrand Laquait tipped his lob over the bar.
Gomis went close again just two minutes after half-time when he drove past Aldo Angoula but fired a powerful shot inches wide of the post.
Evian's response was instant and Lloris had to be at his best once more to turn the ball behind for a corner when Yannick Sagbo met Mohammed Rabiu's cross with a thumping header.
And the hosts took the lead little more than five minutes later through Barbosa. Brice Dja Djedje was fouled but referee Lionel Jaffredo played advantage and Sagbo crossed towards the penalty spot, where Barbosa controlled the ball and fired a left-footed shot on the turn beyond Lloris.
Bastos emerged from the bench and almost made an immediate impact when his cross from the left picked out Gomis but the France international's instinctive shot was well saved by Laquait.
The Brazilian was not to be kept out of the limelight, though, and when Gomis again caused problems for Angoula and was fouled 25 yards from goal, Bastos stepped up to smash the ball left-footed beyond the wall and into the back of the net.
