Surrey elected to bat, but Jonathan Batty's golden duck to Tremlett from the fourth ball of the match meant Ramprakash was at the crease earlier than expected, and needed 18 balls to get off the mark.
His hopes of a historic ton ended when he was caught behind by Tom Burrows off the bowling of left-armer James Tomlinson.
Opener Newman looked to have his eye in until he edged onto his stumps for 42 in the first over of Tremlett's second spell.
Butcher and Afzaal hardly exuded confidence and both benefitted from dropped catches as they began to put together a partnership and steady Surrey's early nerves.
But Afzaal fell lbw to Tremlett for 40 and Butcher (49) was well caught one-handed above his head by Sean Ervine off the bowling of Greg Lamb.
Ally Brown made 27 before being caught by Tom Burrows and Chris Jordan added just two runs to the total.
Matt Nicholson's unbeaten 40 earned Surrey a second batting point, before Tomlinson and Tremlett finished off the tail in time to allow two overs of Hampshire batting.
But the visitors ended on a positive note with Jimmy Ormond claiming the wicket of Carberry from the final ball of the day.