She and Chiyo worked together to beat Sasori, not the Kazekage. Sasori only used the power of the said Kazekage, there are much more to combat than just power and the Kazekage was probably not powerful because his jutsu abilities. Beyond that, Sakura would have died at the start of the fight even before beating the Hiruko doll if it hadn't been for Chiyo.
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Yet Sakura did beat the Kazekage. Sasori was able to use the Kazekage strongest jutsu as its best. Sakura 'never get hitted' worked perfectly in this battle, she really did it.
About Sakura's first punch, it was pretty obvious she was able to heal immediatly. She got a pretty hard hit and was regenerating as soon as she was hitted.
For me, Sakura was impressive. Obviously she wasn't going to make it without Chiyo, but the same goes with our beloved old master. She wouldn't beat Sasori alone, either.