Has an NHL game ever ended 11-4?
It has. 11-4 has been a NHL final 22 times in 70,352 games. The first was Toronto Arenas beat Ottawa Senators on December 22, 1917; the latest was Quebec Nordiques beat Ottawa Senators on March 26, 1995.
That makes 11-4 the 55th most common final score out of 95 that have ever occurred in NHL. One point away, 12-4 has happened 4 times and 11-5 has happened 11 times.