So to update this, the end of NIH's fiscal year was September 30th, and Pitt finished 4th in total total $ funding with $534.1 million for the 2018 FY.
Now that could change as universities can still submit error corrections, but I doubt Pitt's standing will change. For the full sortable list, see
https://www.report.nih.gov/award/index.cfm
The main story here is that Pitt has just had its best ever year in total $ funding compared to peers, surpassing Penn for the first time and hot on the heels of Michigan (John's Hopkins and UCSF are 1 & 2). This does not including $41 million in funding to the Magee-Womens Research Institute, which is composed pretty much of all Pitt faculty. If you combined that, it would put Pitt into 3rd place. However, if you start combining affiliates, then things start to change, because Harvard jumps up to the top, although Pitt's place pretty much stays the same. Pitt, however, still finished 5th in the number of awards with 1,110, which is only 16 grants behind Penn.
Keep in mind that NIH is the most prestigious and competitive source to obtain grants in the health and biomedical sciences. It is very difficult to move at the top of this list as institutions are fairly well entrenched. We'll see if this can be sustained and if Pitt can keep gaining ground, but for now Pitt, for the first time, can boast of being the #1 site of health science and biomedical research in Pennsylvania.