George Bailey's 161 was the third and largest hundred in the visitors' imposing first-innings score of 648 for seven declared on the second day of four at The Oval.
Legendary Sri Lankan batsman Kumar Sangakkara scored the 100th century of his professional career in Surrey's One-Day Cup quarter-final win over Yorkshire at Headingley on Tuesday.
Zimbabwean Sean Ervine rounded off a superb performance by taking the final two wickets to send Hampshire top of the First Division of the county championship on Monday with a crushing win over Warwickshire.
Indian umpire Nitin Menon will be getting a chance to officiate in two English county matches this season as a part of BCCI's Umpires' Exchange programme with England and Wales Cricket Board (ECB).
Pujara was eventually dismissed for 112 of 206 balls, a knock comprising of 14 fours. He, however, will have to wait longer to complete his 12,000 First-Class.
Bailey, who has also played for Middlesex and Sussex, said he was "thrilled" to be returning to Hampshire, who were relegated to the second division in 2016.
Come the end of the season, second-bottom Hampshire and basement club Nottinghamshire were demoted, with Second Division winners Essex going up.
Somerset thrashed a woeful Notts by 325 runs to go top of the table and will be crowned champions if the Yorkshire and Middlesex match ends in a draw.
The Trinidadian last played for West Indies in their limited overs tour of Sri Lanka and has not played a Test in four years nor a first-class game in three years.
Leicestershire won their first home match since 2012 earlier this week.