According to the Blizzard Hearthstone Technical Support Forum, many people are experiencing this issue. I tried posting this solution on that forum, but my posts kept getting taken down [edit: the post has been restored!].
I have only tested this solution on Windows 10, but it may or may not work on Windows 7 and 8.
Lately, I noticed that Hearthstone.exe was consuming more system resources and was causing programs that were running concurrently to lag. I also noticed that Hearthstone.exe would consistently hang when closing. It seems that these symptoms were both introduced with the "Windows 10 Creators Update".
The following are the steps to address this issue on Windows 10 (steps are different and may or may not work for Windows 7 and Windows 8):
Before beginning, run "Windows Update", then search for and install the latest update(s). You may need to restart the computer after installing update(s) before a search yields additional result(s). (Search => Install => Restart => Repeat until there are no additional updates available.)
Right-click on the "Windows/Start Button".
Click on "File Explorer".
Copy and paste "C:\Program Files (x86)\Hearthstone" (without quotations) into the "address bar", and then press "Enter".
Click/Check the "box" next to the words, "Override high DPI scaling behavior.".
(This option is only available with the "Windows 10 Creators Update".)
(For Windows 7 or Windows 8, try checking/clicking the "box" next to the words "Run this program in compatibility mode for:", then click on the "drop-down menu" immediately below and select an earlier version of Windows, then skip to "Step 10".)
Ensure that the "selection" in the "drop-down menu" under the words, "Scaling performed by:", is set to "Application".
After I took these steps, Hearthstone now quits without hanging (sometimes it hangs briefly, but it eventually closes; I tested this many times), and programs running concurrently are no longer lagging.
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