I think that you may use ItemArray property of DataRow:
void Main()
{
DataTable tableOld = new DataTable();
tableOld.Columns.Add("ID", typeof(int));
tableOld.Columns.Add("Name", typeof(string));
tableOld.Rows.Add(1, "1");
tableOld.Rows.Add(2, "2");
tableOld.Rows.Add(3, "3");
DataTable tableNew = new DataTable();
tableNew.Columns.Add("ID", typeof(int));
tableNew.Columns.Add("Name", typeof(string));
tableNew.Rows.Add(1, "1");
tableNew.Rows.Add(2, "2");
tableNew.Rows.Add(3, "33");
tableOld.Rows[2].ItemArray = tableNew.Rows[2].ItemArray; //update specific row of tableOld with new values
//tableOld.Dump();
}