The Linnets limped out of the cup due to a first half goal to continue their poor record against lowly Division One South and West side Borough.
Lynn's fringe side - which had got them this far in the competition - failed to impress, never testing visiting keeper Barclay Lawrencin.
In an awful game on Tuesday, The Walks outfit had plenty of possession but did little with it.
In fact Hillingdon were the main threat early on when Leon Nelson was denied by Lynn keeper Rob Murray in a one-on-one, and in the same situation lobbed tamely over the bar within the first eight minutes.
Borough had kept five clean sheets in their last seven starts, and absorbed Lynn's pressure.
The only goal of the game came on 36 minutes when Murray came out and could only half clear from a cross by Dave Lawrence.
Sam Byfield on the left edge of the box slotted the ball past a defender on the near post into the net.
The second half was no better, Steve Melton having a shot deflected for a corner midway through.
Shortly after came a change with Dean Miller coming on and Michael Frew going up the middle, but Lynn had little cohesion going forward.
In the other semi-final Clevedon beat Didcot after extra time.
Lynn: Miller, Harvey, Lake, Melton, C Defty, Buhlemann, Kelleher (Miller), Fisk, Nolan, Heath-Preston, Frew. Unused subs: Nicholls, Vincent, Keegan, McAnally.
Hillingdon: Lawrencin, Brown, Bennell, Howell, McKenna, Duncan, Lawrence, Kirby, Tilbury, Nelson, Byfield, Not used: Mapes, Wilmott, Murray, Turner, Fitzgerald.
Att:368 Referee Mr S G Burt (Northampton)
Stats, Lynn first: shots on target 1,5: off target 3,1: corners 6,3: offside 1,7; free-kicks 11,14