Smotherman's slam put Purdue (6-2) up 65-63 with 27.9 seconds left. Hammons added two free throws to make it 67-63.
Purdue wasted a 27-17 halftime lead Friday in losing 69-54 to Washington State. One day earlier, the Boilermakers stormed back from a 24-point deficit and pulled within 84-80 on a 3-pointer by Kendall Stephens with 3 minutes left before losing 97-87 to No. 5 Oklahoma State.
"I just thought we had to stay with it throughout the tournament," said Purdue guard Ronnie Johnson, who had 13 points. "That helps our confidence a little bit more, getting this win."
"We're a little undermanned talent-wise," Siena coach Jimmy Patsos said. "Lavon Long and Rob Poole are probably our two best players overall. We played some good minutes, but you have to close it out."
After Poole left, Purdue got six straight points before Hymes got his first points of the second half, a 3-point play, to give Siena a 63-59 lead with 93 seconds left.
Purdue went 21 of 26 from the foul line, while Siena made 13 of 19.
"I thought Siena was quicker to the ball today for 40 minutes," Purdue coach Matt Painter said. "We were fortunate we made our free throws. The difference in the game, we made more free throws. I don't know if we could have said that a couple weeks ago. I think that's a positive from this game."
Poole made consecutive long-range jumpers to give Siena a 58-50 lead with 6 1/2 minutes remaining.
Siena went almost 10 minutes with a field goal before Long's layup gave the Saints a 52-46 lead with 8 minutes remaining. The forward, who had 10 points, fouled out less than a minute later.
After Poole hit a 3 to put Siena up by 16 points early in the second half, Purdue put together a 12-1 run to get within 49-44. The Boilermakers got a pair of in-close baskets from Hammons.
Hymes had 14 points to help Siena take a 43-30 halftime advantage. The Saints led by as many as 15 during the opening 20 minutes.
"We just weren't ready for the first half," Hammons said. "The second half we came out ready."
The Boilermakers beat Siena earlier this season, 81-73 on Nov. 24.