Hours earlier Manchester United had temporarily replaced Rovers as league leader by winning 3-2 at Chelsea.
At Maine Road, however, Shearer struck his 20th goal of the season and Atkins made it 2-0 after 16 minutes to give Rovers an early advantage before Niall Quinn replied for City in the 22nd minute. England left back Le Saux made sure of the points for Rovers by curling in a left-footed free kick in the second half.
Brian McClair killed off a strong Chelsea fightback by scoring the clincher as defending titlist Manchester United gained a 3-2 victory at Stamford Bridge.
Chelsea, which beat United twice in the league last term, hit back from 2-0 down to tie the game with 13 minutes remaining. But McClair silenced the Chelsea cheers a minute later by scoring United's third.
A John Spencer penalty and a header from substitute Eddie Newton tied the game up for Chelsea before McClair's winner.
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