His 84th minute goal cancelled out a rifled shot 15 minutes earlier from Ben Smith, as both sides settled for the comfort of at least getting their respective points tallies rolling after defeats on the opening day.
As a spectacle the match failed to spark for the bulk of the opening 20 minutes, during which time there was only one effort of note on goal.
That came after four minutes when Boston's Ben Futcher saw a header from a Danny Thomas corner superbly blocked by Shrewsbury goalkeeper Joe Hart.
Apart from that it was a tale of tedium until Shrewsbury almost took the lead when Smith broke clear, outpaced Lee Canoville and fired in a low angled drive which Nathan Abbey did well to push over in the 21st minute.
Elsewhere, the only other real attacking initiative came from two Thomas crosses and a couple of optimistic off-target efforts from distance by Brad Maylett as Boston faltered on a well-drilled Shrewsbury back line.
On the stroke of half-time the visitors threatened again when Neil Sorvel unleashed a shot from distance, but Abbey held on securely.
There was a touch more life at the start of the second half with Boston lifting the tempo, as Stewart Talbot saw a 20-yard shot blocked by Sorvel and a 25-yard Maylett free-kick flew straight at Hart.
The home momentum continued on 65 minutes when, at the end of a flowing move, Lee's left-foot shot on the turn was tipped over by Hart.
But it was Shrewsbury who went ahead on 69 minutes when Mark Stallard surged down the left and fed the ball inside to Smith, who crashed a low 18-yarder past Abbey.
Boston threw on midfielder David Noble at the expense of defender Austin McCann in a bid for late salvation.
And the home leveller came six minutes from time when Canoville burst down the right and crossed low for Lee to stab in from close range.
Boston almost snatched a winner on the stroke of full-time when Lee headed back a Canoville cross and Thomas fired against a post with a spectacular overhead kick.