Can I bring a dram shop claim against a bar or restaurant so they can be held liable for damages caused by an intoxicated patron?

Yes. This is called a Dram Shop Claim. Under Minn. Stat. § 304A.801, a liquor establishment (usually a bar, restaurant, or liquor store) can be held liable for injuries stemming from the intoxication of the drunk driver, if the sale was illegal.
Generally, illegal sales include:

1. Sales to a minor.
2. Sales to an obviously intoxicated person.
3. Sales made during a prohibited time of day/day of the week.

More information on Dram Shop claims can be found here.