Marriage certificates at that time usually contain parents' names:
http://www.nyc.gov/html/records/html/vitalrecords/marriage.s...

If you do not want to pay for a certified copy, you can obtain a photocopy from the Family History Library in Salt Lake City with the information you have. You can also order a copy of the death record here as well. But you will have to know the film number it is on.
http://www.familysearch.org/eng/search/rg/images/freqmicrofi...