Juan Dixon had 29 points in 10-17 shooting as he moved within 7 points of the all-time record at Maryland. Steve Blake added a double-double with 11 points and 11 assists for the Terrapins.
James Clinton led Siena with 16 points, Dwayne Archbold added 14 and Andy Cavo 13 in the defeat.
Maryland used several runs in the first half to build up a 52-38 halftime lead. After holding a 18-17 lead with 14:40 to go in the first half, Maryland went on a 15-3 run as Baxter had two dunks for four points and Drew Nicholas scored a three and the foul for a rare four point play for a 32-21 Terps lead.
Then, Siena got back within 9 before Dixon nailed 2 three-pointers and had 7 points in a 14-4 run.
At the end of the first half, Siena scored the final nine points to trail 52-38 at halftime. After the Saints scored the first two baskets of the second half, Maryland responded with a 15-2 run with 6 points by Dixon and 5 by Steve Blake to put the game away.
Maryland will now advance to play the Wisconsin Badgers for a trip to the Sweet 16 on Sunday.