Brett Harvey scored 15 for Loyola (2-6, 0-1), which has lost three in a row.
Alex Franklin scored 21 points and Edwin Ubiles added 20 to lead Siena (3-3, 1-0).
After trailing by as many as 11 in the early minutes of the second half, Loyola cut the deficit to 51-48 on a coast-to-coast layup by Harvey with just less than 11 minutes to play. Then Barney's layup in the paint trimmed the Saints' lead to 52-50 at the nine-minute mark.
Loyola tied the score at 54 with 7:26 left on a jump shot by Brad Farrell. But Siena responded with a 14-2 run over the next 4:30 to go up by 12 and seal the win.
"We played tough, and Siena's experience really helped them tonight," Greyhounds coach Jimmy Patsos said. "This is how you get good - by playing good teams. I believe in our young players because they are the future of our program."
The Saints led 36-28 at halftime. Isaac Reid had nine points and four rebounds for Loyola in the first half. The Greyhounds pulled within 22-21 on Barney's layup with just less than seven minutes left in the first, but Siena closed on a 14-7 run.
Loyola's bench players outscored their counterparts 23-8, and the Greyhounds won the rebounding battle 38-28.
The Saints made 26 of 51 field goals.
Kenny Hasbrouck added 13 points for the Saints (3-3, 1-0), who bounced back after three consecutive losses in the Old Spice Classic over the weekend.
Loyola continues conference play at noon Sunday against Niagara at Reitz Arena.