Aside from playing a Barbarian or a Monk, using a shield can potentially block out a lot of damage and give you a better chance of surviving.
But the most important thing in HC that helps combat lag spikes and DC, is passive life gain; in other words, Life Regeneration. Boost you EHP and get 1000+ Life Regeneration and use the Inspiring Presence passive if you are a Barbarian.
For followers, Enchantress with a Maximus or the Scoundrel with a Windforce or Buriza-Do Kyanon should provide an extra layer of defense.
Your best bet though, is to be in a good group to avoid being defenseless during a DC.
Enchantress with the Maximus, having a million or more EHP, and hit the esc key and take a deep breath before returning to game. There is little for newer players to do but if you area level 60 player, there are some options but not all are viable to the average player. For some it all just comes down to luck.