Here are couple of ways to solve this:
This first method is a way to do this without having to have a flag that indicates "inside the record".

#!/usr/bin/perl
use strict;
use warnings;

while (<DATA>)
{
    process_record($_) if /^Success\|Filter passed/;
}
sub process_record
{
   my $trigger_line = shift;
   print "$trigger_line";
   print while (defined ($_ = <DATA>) and $_ =~ /\S/);
   print "\n";
}


__DATA__
Success|Filter passed|[invalid field]|[invalid field]|Id-350a875b08796
+5e58cbe1f4a 
Accept: text/plain, text/plain, application/json, application/*+json, 
+*/*, */* 
Host: api2.tim.com.br 
User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.3
+6 (KHTML, like Gecko) Chrome/52.0.2743.116 Safari/537.36 
Via: 1.1  
X-Forwarded-For: 144.22.98.123 
X-Forwarded-Host: 
X-Forwarded-Server: 

Success|Success in calling policy shortcut|[invalid field]|[invalid fi
+eld]|[invalid field]|Id-350a875b087965e58cbe1f4a|Call 'Set Request Me
+ssage'|GET 
Accept: text/plain, text/plain, application/json, application/*+json, 
+*/*, */* 
Host: api2.tim.com.br
User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.3
+6 (KHTML, like Gecko) Chrome/52.0.2743.116 Safari/537.36
Via: 1.1 api2.tim.com.br 
X-Forwarded-For: 144.22.98.123 
X-Forwarded-Host:  
X-Forwarded-Server:  
Content-Type: text/xml; charset="UTF-8" 

Success|Filter passed|[invalid field]|[invalid field]|Id-350a875b08796
+5e58cbe1f4a 
Accept: text/plain, text/plain, application/json, application/*+json, 
+*/*, */* 
Host: api2.tim.com.br 
User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.3
+6 (KHTML, like Gecko) Chrome/52.0.2743.116 Safari/537.36 
Via: 1.1  
X-Forwarded-For: 144.22.98.123 
X-Forwarded-Host: 
X-Forwarded-Server:
[download]

Another way...
Perl has a special operator that will keep track of the "inside the record" flag for you..

#see https://www.perlmonks.org/?node_id=525392

while (<DATA>)
{
    print if (/^Success\|Filter passed/ ... /^\s*$/);    
}
[download]