Constable's header, his 99th goal for the club, gave the visitors a fifth-minute lead, while Smalley's late penalty made sure of the points.
But in between the U's had to defend for their lives as Wimbledon poured forward in search of a way back into the game.
The back four were outstanding and thoroughly earned their fourth successive clean sheet in League Two.
A fifth win in seven away games ensured the U's will head into November top of the table.
Asa Hall replaced the suspended Dave Kitson in the only change to the side which started the goalless draw with Exeter City in midweek.
It prompted a change of shape, with Andy Whing sitting deep in a 4-3-3 which saw Sean Rigg and Ryan Williams pushed up on the flanks to support Constable.
Heading into the game the U's had failed to find the net in almost four hours of League Two football, but it took them just five minutes to end the run.
Hall robbed Peter Sweeney just outside the penalty area and crossed for an unmarked Constable to head in his fifth goal of the season.
Danny Rose also curled a free-kick over in a promising opening for the visitors, before Wimbledon went on to have a good spell.
Their main threat came from George Porter on the right flank. He stretched Tom Newey on 13 minutes and fired a centre across the face of goal, just ahead of George Francomb.
United were forced to defend a host of balls put into the box, but Michael Raynes and Jake Wright held firm.
The visitors were happy to soak up pressure and play on the break.
On the half hour they should have been awarded a penalty, when Rigg was floored by Barry Fuller when through on goal.
United waited for referee Dean Whitestone to point to the spot, but astonishingly he allowed play to continue.
Wimbledon looked vulnerable when attacked at pace and Williams quickly exposed the defence with a mazy run, but his shot was saved by goalkeeper Ross Worner's legs.
The hosts' best moment of the half came ten minutes before the break. Porter was again the architect, crossing for Michael Smith to send a diving header just over Ryan Clarke's crossbar.
The half ended with Rigg having another good shout for a penalty turned down as Fuller again halted his progress, while Newey picked up a fifth booking of the season, and with it a one-game suspension, for time wasting.
Constable laid on the first chance of the second half with a superb touch to Williams, who rushed the chance and shot wide.
It was a rare sight of goal for the U's early in the second half, as Wimbledon built up a head of steam.
Clarke made his first save of the game from Francomb seven minutes into the half after some indecision from Raynes.
United's defence had to work overtime as Wimbledon bombarded their penalty area.
There were plenty of nervous moments, but the back four performed well to restrict the chances.
As the hosts increasingly took risks to get back into the game, United had space to exploit in the break.
With 20 minutes left Smalley, on as a substitute, ran on to a through ball from David Hunt. He unselfishly squared for Constable, who blazed over with the goal gaping.
A superb passing move five minutes later set up an opening for Danny Rose, who could not hit the target.
Kevin Sainte-Luce gave the Dons menace on the right after coming off the bench and Clarke needed to be alert to block a shot from the winger after a dangerous run.
It was a precious save, as United went on to extend their lead nine minutes from time.
Josh Ruffels' ball over the top saw Smalley beat Rhys Weston, who then fouled him in the box.
The striker dusted himself down and blasted home from 12 yards to give the visitors some breathing space for the first time.
United still had to defend well in the closing stages, but held on to their clean sheet to complete a productive afternoon.
Oxford Utd: Clarke, Hunt, Raynes, Wright, Newey, Williams (Smalley 61), Whing, Rose, Rigg (Ruffels 80), Hall (Davies 59), Constable.
Unused subs: Crocombe, Bevans, O'Dowda, Marsh.
Wimbledon: Worner, Fuller, Weston, Frampton, Kennedy, S Moore, Sweeney (Pell 76), Francomb, Porter, Strutton (L Moore 63), Smith.
Unused subs: Brown, Fenlon, Sainte-Luce, Midson, Antwi.
Referee: Dean Whitestone (Northamptonshire).
Attendance: 4,685 (854 visitors).