Boulter, bidding to reach a seventh quarter-final on grass, had expressed concern about her serve earlier in the week, suggesting she would be working on it in the build-up to this match.
But no such troubles were apparent in the opening set against Shnaider as Boulter continually caused problems behind her first serve.
Having saved a break point, then secured an impressive break to love with a crowd-pleasing volley, Boulter battled to consolidate with an important hold and saved another break point along the way.
She then took the double break with a sweeping forehand, before more solid serving handed Boulter the opening set as rain threatened to come down.
But by the time the umpire suspended play because of a downpour, Boulter was down a break at 4-1 in the second set and in trouble on serve again.
After a 20-minute rain delay, she returned to have her serve broken for a second time and, despite recovering one break, she could not prevent Shnaider from forcing a deciding set.
Boulter once again came under pressure in the opening game, wiping out three break points to secure the hold as problems on serve returned with a vengeance.
She saved more break points in her next service game, only to double-fault and concede the break.
From there, Boulter struggled to regroup and went down a double break.
She could not find a way back from there, missing out on a fifth quarter-final in a WTA 500 event as Shnaider set up a meeting with American second seed and Australian Open champion Madison Keys.
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