Callum Thorp’s second delivery saw an early wicket with Suppiah caught by Borthwick with Somerset 4-0 but that was to be the highlight of the first two sessions for Durham supporters after Trescothick and Compton raced to build a quick 150 partnership.
The Durham attack battled on without reward and the Somerset skipper brought his hundred up with a huge six, having scored 84 of the runs from boundaries and sixes from 128 deliveries.
Along with Compton he batted fluently until just before tea when he sent the ball soaring up towards point, which Ruel Brathwaite caught with a dive forward, at which point he was dismissed on 144 with Somerset 253-2 just before tea.
At the break the visitors were 259-2 with Compton 92* and Hildreth 5*
Compton drove Borthwick through the covers to reach pass hundred at the start of the final session and Hildreth scored quickly and pulled Benkenstein for six to reach his fifty, which also included ten fours, off 46 balls
Graham Onions claimed the third wicket, that of Hildreth, who was caught behind on 54, off the third ball of Onions third spell with the Somerset total at 340.
The new ball was taken after the third wicket fell and Onions was rewarded again in his next over when Barrow (4) nicked the ball to Gordon Muchall at first slip.
At the close of play Somerset, having batted well all day, were 383-4 with Buttler 9* and Compton 149*.
Durhamccc.co.uk caught up with returning skipper Phil Mustard at the close of play, “I still think it was a good decision to field first, especially on that side of the wicket because it always does a little bit early on but we just didn’t get the ball in the right area enough.
“Trescothick is a really frustrating player, because he plays the ball late, watches the ball and keeps nudging it down to third man – it’s a pleasure to watch him, just not when it’s against your team.
“It’s frustrating that we missed a couple of chances today, especially after all the hard work we put in out there. It’s not the first time we’ve dropped a couple of catches but we need to hold on to them because they can change a game.
“We’ve got to contain them and try to encourage them to make mistakes, we’ve got four down today and we’re seen earlier in the season that they can collapse from that point. If we make a good start in the morning we could bowl them out for 450-460 and that would be fantastic.
“We need to do what we did against Warwickshire last match – the first two or three days were tough for the team but it showed that if you dig in deep and for long enough you can get results.”