The American top seed was well below her best, but beat unseeded Dutch player Bertens 7-6 (9-7) 6-4.
Spanish fourth seed Muguruza impressed in a 6-2 6-4 win over former finalist Sam Stosur of Australia.
Both matches were watched by sparse crowds on another cold, grey day as Paris suffers severe flooding.
Williams, 34, is aiming to tie Germany's Steffi Graf on 22 major singles titles, which would put her two behind all-time leader Margaret Court of Australia.
Williams out of sorts but into final
Defending champion Williams had made a host of errors in her quarter-final and was unusually inconsistent again as she faced an opponent making her Grand Slam semi-final debut.
Both women went into the match with injury doubts - Bertens struggling with her calf and Williams reportedly playing through a thigh problem.
Bertens, ranked 58th, had plenty of chances in the first set against a sluggish Williams, earning seven break points and two set points, but Williams came back from 4-2 down to clinch it in an unpredictable tie-break.
Two dreadful volleys, one of them on set point, illustrated Williams' lack of form but experience dragged her through, and she came back from a break down to take control of the second set.
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