MySQLdump leads to exceeding max connections. Skip-Quick as a solution?
mysqldump takes only 1 connection.
There is 1 extra connection for root.  (Note the 151 vs 152.)  I hope you are not using root for your app; change that if you are.  Then allow mysqldump to be the only root process running when it is doing a dump.
Limite the number of connections requested -- by adjusting the web server (or whatever is doing connections).  Web servers tend to allow far more children than is efficient.
Disconnect (in the app) from MySQL when finished processing.
Lower wait_timeout -- this will lead to disconnecting idle threads or threads that are held unnecessarily long by a &quot;connection pool&quot;.
Running mysqldump takes resources away from other queries; be sure to run it at off times.
Use the slowlog to find out what queries are the most impacted by the dump; then let's discuss improving them.
If you have an LVM snapshot, why bother with mysqldump?  LVM is so much faster and less invasive.