Former New Zealand batsman Spearman made 109 on a rain-affected day and was twice reprieved on his way to three figures by England's Marcus Trescothick.
In the day's other Championship match, last season's first division runners-up Hampshire collapsed to 139 for seven on a rain-marred day against Lancashire at Old Trafford.
The home side's 20-year-old seamer Tom Smith led the Lancashire attack with three for 29.
But at the County Ground, Trescothick had a fraught comeback after returning home early from the tour of India, the Somerset opening batsman twice dropping Spearman at slip when the batsman had made 36 and then 92.
Spearman, though, was not complaining after hitting two sixes and 14 fours in his 177-ball innings.
"I didn't really expect to score a hundred," the 33-year-old Spearman, who played the last of his 19 Tests for New Zealand in 200, said.
"I gave a couple of chances. On 36 I should have been out, and I got away with another one later. But all in all, I'm delighted," added Spearman who two years ago scored 341 for Gloucestershire against Middlesex in the County Championship, eclipsing a 128-year-old record previously held by cricket great WG Grace for the highest score by a Gloucestershire player.
But even before Spearman opened the innings Tuesday any hopes he or anyone else might have had of winning the Walter Lawrence Trophy for the fastest first-class hundred in an English season had been all but ended by Nottinghamshire's Mark Ealham.
The former England all-rounder smashed a 45-ball hundred for the county champions in the traditional curtain-raiser against MCC at Lord's last weekend, where Ealham ended on 112 not out in a match Nottinghamshire won by 142 runs.
The fastest-ever first-class hundred in the Walter Lawrence Trophy, since the format was changed in 1985 to balls faced as opposed to minutes, was scored by Tom Moody in 36 balls for Warwickshire against Glamorgan at Swansea in 1990.
However, this was before an adjudication panel ruled that centuries should not be considered a genuine achievement when 'declaration' bowling was involved, making Ealham's the fastest authentic first-class century in an English season for 21 years.