Poulsen completed his double in the space of five minutes early in the first half while Werner added two more late in the second half to send Leipzig five points clear of fifth-placed Eintracht Frankfurt.
Leipzig, whose victory was a big boost for their confidence after their Europa League exit in midweek, are on 28 points.
Borussia Dortmund lead the standings on 39 after notching up their sixth straight win on Saturday, a 2-1 victory over Werder Bremen.
Champions Bayern Munich are third on 30, level on points with second-placed Borussia Moenchengladbach.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
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