Boulton himself hit nine 180's and looked to have the 'X Factor' but Baggish kept plugging away and in the deciding set produced the right darts at the right moments to set up a tie with Nathan Aspinall.
Baggish started well claiming an early break; as well as also claiming a hold of throw to make it 2-0 in the early going.
Boulton though plucked out a 120 checkout out of nowhere; putting the impetus back onto Baggish to win the set on his throw.
Two 180's in the requisite leg though handed Boulton a chance at the decider on his throw; as the Ardrossan ace began to play really well.
A 54 checkout saw Baggish roar and jump around with the crowd; as he claimed the set and soaked up the adulation of the crowd.
In the requisite set, Boulton led and hit a sixth 180; but Baggish from there hit a brilliant 84 checkout on double 18 in order to lead 2-1; but Boulton tied it up. Despite that Baggish had the throw anyway; so looked to potentially register a set on the board.
A 180 and a 76 checkout saw Baggish in quick fire fashion register this set; to make it 1-1 and leave it finely poised.
He continued to find his rhythm but despite having multiple chances to break; he couldn't and Boulton was given opportunity to hold his throw.
Baggish missed further darts at double to hold and Boulton helped himself to a break of throw and looked to be cruising towards the set.
Despite that, it turned again with Baggish halving the deficit and he made it 2-2 from there but it was Boulton that had the throw.
He used that throw to pin double 20 to go 2-1 up in sets. On Baggish's throw, Boulton again was given further opportunities to break but the Guam native held his throw with a 65 finish on double 20.
Boulton hit a 51 checkout to hold his throw in what as a result was an integral part of the game. A 25 checkout saw another break of throw and from there Baggish finished the set with a 100 checkout to send it into a fifth and final set.
Boulton took the first leg of the final set with a 130 checkout; but Baggish hit an 80 checkout to soon go one away and he finished the job off.
Click here for more information on the PDC World Championship, which takes place at the Alexandra Palace between December 13 and January 1.
Arron Monk (82.56) 0-3 (88.64) Jose Justicia (R1)
Andy Boulton (85.12) 2-3 (84.94) Danny Baggish (R1)
James Richardson vs Mikuru Suzuki (R1)
Michael Smith vs Luke Woodhouse (R2)
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