The second-seeded Terrapins (25-12) will face the winner of Wednesday's quarterfinal tilt between Iowa and ACC rival Virginia.
Alex Len led the way for Maryland with a double-double of 14 points and 13 rebounds. Dez Wells and Jake Layman both added 13.
Maryland shot 50 percent from the field and led 31-24 at halftime. Alabama overcame tepid shooting in the first half and dogged Maryland the rest of the way.
Trevor Releford scored on a layup for Alabama with 47 seconds to play, but failed to convert two final field goals in the closing seconds. Maryland did not score in the final 2:10 of the game.