Substitute Yattara opened the scoring in the 77th minute and Ligue 1 top scorer Lacazette took his tally to 25 eight minutes later to move Lyon up to 64 points from 32 games.
French champions Paris St Germain, who have one game in hand, are second two points off the pace.
Lyon dominated throughout but were made to wait by Bastia, who were reeling from their 4-0 defeat in the League Cup final against PSG last Saturday.
Lyon's Jordan Ferri dribbled past a defender before his curling shot was superbly saved by Alphonse Areola in the sixth minute.
Areola was at it again when he blocked Steed Malbranque's back heel on the half hour and tipped away Clinton Njie's low shot three minutes before the break as Lyon continued to dominate.
Malbranque was substituted in the 62nd minute and replaced with France international Clement Grenier, who was making his comeback after an eight-month injury layoff.
Nabil Fekir was not having his usual influence in the Lyon midfield and was replaced in the 74th minute with Yattara, who had an immediate impact, scoring three minutes later with a shot on the turn from Grenier's pass.
Lacazette wrapped it up from close range five minutes before fulltime, converting Njie's cross from the left.
(Reporting by Julien Pretot; Editing by Toby Davis)
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