In appalling conditions, Boro produced a disciplined display but rode their luck at times particularly in the opening stages.
The Dutch side appeared to have taken a 13th minute lead when the Moroccan Tarik Sektioui fired into the net after Brad Jones had parried two shots, only to have the effort controversially disallowed.
Mark Viduka's effort from a difficult angle was then blocked by Alkmaar keeper Henk Timmer who also had to be alert to deny Szilard Nemeth in the 21st minute after the Slovakian had been sent clear by Jimmy Floyd Hasselbaink.
Jones gathered Kenneth Perez's deflected free-kick and in an entertaining first half Shota Arveldaze glanced a header narrowly wide when the former Rangers man should perhaps have done better.
Jones also pulled off the save of the match midway through the first half when he got down well to keep Perez's snap-shot out.
Despite the incessant rain the two teams produced a fine spectacle in the first period, but the second half was more mundane.
After a quiet start to the second period, George Boateng was fortunate to escape with a booking after a rash challenge on Gretar Steinsson.
Chris Riggott floated a 62nd minute header over the bar while at the other end, after a goalmouth scramble, Barry van Galen looped a close-range shot too high.
With 20 minutes left Boateng's snap-shot was well-saved by Timmer down to his right but it was Louis van Gaal's side that went closest to snatching all three points in the closing stages.
Jones was relieved to see Ugo Ehiogu block van Galen's effort after the Australian keeper had punched the ball weakly away and with three minutes left Danny Koevermans' effort was cleared off the line but Boro survived.