Jacob Duffy, one of three debutants for the New Zealand side this week, believed the bowling unit has worked well as a team.
"We are in a really strong position," said the 20-year-old. "It is obviously a hell of a way to start the tour against tough opposition, in conditions that haven't been easy."
This morning, all eyes were on Santner when the New Zealand XI resumed on 149-3. The 23-year-old was on 70 and looking to bring up his maiden century for his country.
The young talent from Northern Districts was made to work for every run and took his chances with his trademark free-flowing shot making.
He stalled when he closed in on the milestone and was in the 90s for seven overs. Santner looked to break the shackles with a cover drive, got a thick outside edge and was caught in the gully by Peter Trego on 94.
"I was pretty happy with the way I played but obviously pretty disappointed to not get 100," Santner said afterwards.
Santner said the Somerset attack bowled well this morning and the pitch was "still doing a bit". He still looked comfortable out in the middle.
"I was nervous. There are always going to be nerves in your first game [for New Zealand] but they eased once I got a few shots away. It was a good day and hopefully there are a few more games for New Zealand to come for me."
Watling, who top scored with 65 in the first innings, steadied the ship once again and combined with Mark Craig (20) and Doug Bracewell (16) to continue the momentum.
Wheeler, the hero with the ball in the first innings, provided some chaos with the bat at the tail of the innings.
When Watling departed, the 23-year-old flicked the switch. He hit 33 runs from only 16 balls, including two towering sixes, to finish with a flourish.
Somerset's Tim Groenewald, who picked up a four wicket bag in the first innings, was again the pick of the bowlers for the home team with 5 wickets for 65 runs from 18.5 overs.