The setting used for this Mass was the famed Missa Papae Marcelli of Palestrina. It was sung by the Lassus Scholars under the direction of Ite O'Donovan.
One of the most glorious pieces of that setting -- in my own estimation -- is the Kyrie. Here it is. (Unfortunately you will only get a very brief views of the liturgy itself at the beginning.)
Here, also, is the Gloria: