Hampshire were eventually all out for 512, Ben Phillips finishing with 4-75, before Somerset closed on 104-2.
After resuming on 132-2, the hosts were bowled out for 286, with Ben Phillips picking up 4-60.
Justin Langer's 88 and Ben Phillips' unbeaten 53 enabled Somerset to declare their second inning at lunch on 243-8.
Ben Phillips (2-20) did the early damage, bowling the dangerous Jim Allenby before having big-hitting Australian opener Mark Cosgrove caught behind.
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John Crawley had earlier taken his overnight score of 78 to 104 before becoming one of three victims for Ben Phillips (3-62).
Batting first at Nevil Road, the home side were quickly in trouble at 27-4 and then 51-5 thanks to Alfonso Thomas (4-18) and Ben Phillips (3-24).
When Hoggard took the second new ball the target was down to 73 with 21 overs left but he quickly bowled Ben Phillips middle stump for seven.
Somerset seamer Ben Phillips, who took 3-31 in his team's opening match, saw his first two balls hit down the ground for four and six by Perkins, before Simmons sliced the final ball of the over to third man.
James Hildreth never looked entirely comfortable in making 14 off 30 balls before falling lbw to Martin-Jenkins and it was 39-3 when the decision to promote Ben Phillips in the order backfired as he was bowled by a full-length ball from Yasir Arafat.
They also confirmed their two other long-term injury victims Mike Phillips and Ben Lewis will return on time.
At outside half, Gatland will have Owen Farrell and Jonathan Sexton, while his scrum half options will be Conor Murray, Mike Phillips, and Ben Youngs.
Chelsea made a double switch with 17 minutes left, sending on Tal Ben Haim and Shaun Wright-Phillips for Ashley Cole and Joe Cole.
Injuries to Kristian Phillips, Gareth Owen and Cai Griffiths will be monitored, Ben Lewis is out until November, but Richard Hibbard could play a part after featuring in Aberavon's loss at Llanelli last weekend.
The EHRC was hit by a series of resignations over the summer, and several public figures including the head of Stonewall , Ben Summerskill, and president of Mencap , Lord Rix, have called on Trevor Phillips to resign.
Phillips and Colin Greening also scored for the Senators, who got 32 saves from Ben Bishop.
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