The former world number one and five-time Grand Slam winner too just over an hour to win 6-3, 6-1 in China.
Sharapova lost her first service game but fought back to draw level before going on to take the opening set with a hold to love.
Sharapova closing on first title since ban after reaching Tianjin quarters
Voegele presented Sharapova with three match points when she made her eighth double fault when serving at 5-1 down and the Russian sealed the match with a forehand winner.
Sharapova, targeting a first title since returning to the tour in April following a drugs ban, will face third-seed Peng Shuai of China after she thrashed Sara Sorribes Tormo 6-0, 6-1.
In the other quarter-final tie, Aryna Sabalenka beat local hope Zhu Lin 6-3, 6-4 and she will play the winner of the match between Christina McHale and Sara Errani.
Garcia pulls out of Tianjin Open with injury
'Great to practise with Andy Murray and hopefully he's back soon' - Djokovic