Pierse needed 19 holes to defeat the 59-year-old Bogan, who held an early lead and failed to capitalize on many opportunities.
'He should have been 3 or 4 up on me but I kept holing out and getting up and down,' said Pierse, who represented the Great Britain and Ireland at the 1983 Walker Cup Match.
Pierse, 56, will next play Wisconsin native Stu Grendahl in the quarterfinal round on Wednesday.
Grendahl downed David Stanfield in the other 19-hole match of the round.
Logan Jackson, 57, defeated 2002 Senior Amateur champion Greg Reynolds, 4- and-3. He will next play Stanford Lee, who beat James Butler 5-and-4.
In the Lower Bracket, Vinny Giles beat Bill Zylstra 3-and-1 to force a quarterfinal match against Sam Farlow, a 6-and-5 winner against Donald Marsh.
Giles was the 1972 U.S. Amateur champion.
Also, Alistar Catto beat Larry Grant 3-and-2 and will next face Frand Ford III, who beat Donald Bliss, 3-and-1.
There will be two rounds of match play again on Wednesday. The 18-hole final will take place Thursday