Eger tallied his first Champions Tour win in nearly five years, and his third overall, as he shot a 3-under 69 in the final round, finishing the tourney with an 11-under 205, one better than Armour's minus-10.
The two golfers were tied for the lead deep into the final round but Armour faltered when he bogeyed the 17th hole while Eger birdied the 16th for a two-shot lead.
Eger finished with a bogey at 18, but still managed to win by a stroke.
Armour ended with a 5-under 67 Sunday to finish at 10-under 206. Tom Kite (69) took third at 8-under 208, followed in fourth place by David Peoples (68), Fred Funk (69) and Mark James (69).