Extreme haustorial parasites have long captured the interest of naturalists and scientists with their greatly reduced and highly specialized morphology. Along with the reduction or loss of photosynthesis, the plastid genome often decays as photosynthetic genes are released from selective constraint. This makes it challenging to use traditional plastid genes for parasitic plant phylogenetics, and has driven the search for alternative phylogenetic and molecular evolutionary markers. Thus, evolutionary studies, such as molecular clock-based age estimates, are not yet available for all parasitic lineages. In the present study, we extracted 14 nuclear single copy genes (nSCG) from Illumina transcriptome data from one of the "strangest plants in the world", Hydnora visseri (Hydnoraceae). A ~15,000 character molecular dataset, based on all three genomic compartments, shows the utility of nSCG for reconstructing phylogenetic relationships in parasitic lineages. A relaxed molecular clock approach with the same multi-locus dataset, revealed an ancient age of ~91 MYA for Hydnoraceae. We then estimated the stem ages of all independently originated parasitic angiosperm lineages using a published dataset, which also revealed a Cretaceous origin for Balanophoraceae, Cynomoriaceae and Apodanthaceae. With the exception of Santalales, older parasite lineages tend to be more specialized with respect to trophic level and have lower species diversity. We thus propose the "temporal specialization hypothesis" (TSH) implementing multiple independent specialization processes over time during parasitic angiosperm evolution.