If you change your password to a site that had been saved, Google with automatically prompt you to ask if you wish to update/save the password for the current site. Enter the new password in the proper pop-up message fields and click save.
An alternate way is to delete the saved password and when logging into a site, manually enter the new password then click save to save it in the browser. To delete a save password, do the following steps:
Step 1. Open the Google Chrome browser
Step 2. Open the menu by clicking on the three dots 
in the upper right hand corner. Click on/select settings.
Step 3. In the Autofill section, click on Passwords.
Step 4. Locate the save login that needs to be updated. Once found click on the three dots to the right of the listing. Select remove.
Step 5. Go to the website to log in with your password, select save in the proper pop-up message fields and click save.