Santos had come on as a 60th-minute substitute in place of Branko Boskovic, and he leveled the score in the 72nd minute. Santos tried a left-footed shot from outside the penalty area that skipped past the futile dive of Donovan Ricketts and into the corner of the net.
Santos thought that he had given United the win in the final minute of normal time, but he was correctly ruled offside as he buried Dwayne De Rosario's cross from the right wing.
United has not won two consecutive MLS games since 2009.
There is no score at halftime between one of MLS' founding clubs and its newest expansion team. D.C. United and the Montreal Impact have shown plenty of endeavor, but not a lot of finishing product as they struggle for chances on a damp, cool night at RFK Stadium.
Indeed, the offensive displays by both clubs have been so abject that neither team has managed a shot on target, while Montreal forward Sanna Nyassi, the greatest individual threat for either team, has been flagged for offside three times.
The fans at RFK observed a moment of silence during the 12th minute of play for longtime D.C. United fan Javier "Chico" Solares, a member of the club's Barra Brava tifo group who passed away Tuesday evening.