The visitors were 158 for four at the close of a rain-affected second day, chasing New Zealand's first innings of 441 after the home side's tail had wagged and added 134 runs to their overnight score for their final four wickets.
Anderson then chipped in with two quick wickets and pulled off a diving catch at point to dismiss the dangerous Shivnarine Chanderpaul for four as the hosts seized the advantage after the second day which lost 27 overs of play due to rain.
"I think it's a pretty good track so we're going to have to bowl well in the morning to take these next six wickets and try to get into a position where we can win the game," Anderson told reporters at the Basin Reserve.
"I think we're in a good position at the moment ... (but) we still have a lot of work to do."
While New Zealand's bowlers had captured wickets at critical times in the lengthened evening session after rain had washed out the entire afternoon, West Indies were scoring a little too freely for their liking, Anderson said.
The visitors had belted 22 boundaries in their 158 runs after Tim Southee and Trent Boult had initially put them under intense pressure at the start of their innings.
The biggest concern for the hosts is Marlon Samuels, who was 50 not out having hit nine boundaries from 57 balls and had been particularly punishing on leg-spinner Ish Sodhi with three boundaries.
Sodhi's three overs, one of which was a maiden, cost 18 runs with Samuels scoring 17 of them.
"Obviously they've scored a few more runs than we would have liked," Anderson said. "I think we gave away too many four balls today.
"If we take a couple of poles (wickets) in the morning, then we'll be sitting in a good position."
Anderson, who scored 38 on the first day, was pleased with the contribution with the bat of the team's bowlers, which had pushed them past 400 and he had special praise for wicketkeeper BJ Watling who marshalled the tail.
Watling, who was last man out for 65, shared in three partnerships with his bowlers with the highlight a 58-run final wicket partnership with Trent Boult, who blasted 38 not out.
"It's nice to think that our tail is wagging a lot more now," Anderson said. "Its nice to have guys chip in with 20s or 30s and Boulty obviously had 38 not out at the end there so it always helps.
"I guess it doesn't demoralise an opposition team but it just saps, or takes a little bit more energy out of them, knowing that they're so close to finishing but they can't finish the job.
"So it was nice to get that kind of score to give us a bit of a buffer."