Root (71) fell just short of a new Test-best, in the first century stand of the match with Jonathan Trott (56), after Anderson had created an opportunity for England to take charge by completing his 13th five-wicket haul - but Tim Southee (three for 34) kickstarted New Zealand's fightback in an absorbing contest.
Anderson (five for 47), fresh from passing 300 Test wickets on Friday, and Steven Finn (four for 63) did most of the damage as the tourists lost their last six wickets for 52 to be bowled out for 207.
Then after both England openers went with the score on 36, Root and Trott took over - until Southee, who had spent much of the evening session off the pitch with a hand problem, returned to see off Root, Jonny Bairstow and then Matt Prior in a stumps total of 180 for six and limit the home lead to 205.
Root, playing in his first Test match in England, said he was disappointed not to go on and again a hundred after being well set.
He told Sky Sports: "I was very disappointed not to kick on and after giving them a sniff tonight, we're quite down about it. We need to get going tomorrow.
"It's quite a slow pitch and you've got to really work hard to start with and get going really."
Root is batting at No 4 in the match, the position normally occupied by Kevin Pietersen, who is injured and ruled out of the two-match series.
The 22 year old opens for his county side Yorkshire and there is speculation that is where he could end up playing for his country eventually.
But Root said he is not fussed where he bats for his country.
I just enjoy playing and to get the opportunity to represent your country is fantastic and whether that means batting middle order or opening, it doesn't really bother me," he added.
Alastair Cook was first to go on in England's second innings, falling to Trent Boult when Dean Brownlie took an outstanding catch diving to his left at third slip.
Nick Compton was then bowled through the gate by a Neil Wagner inswinger, before Trott and Root shared a seamless stand in which only their inexplicably faulty running between the wickets gave the Kiwis much hope.
The Kiwis did not bowl well at Root, giving him the freedom to score freely square of the wicket on the offside on the way past a 78-ball 50 which contained six fours.
His only scrapes came with a series of misunderstandings with Trott over singles, and a direct hit would have run him out three times between 30 and 54.
It was not until Southee returned that the young Yorkshireman succumbed, bowled off an inside-edge on the forward-defence to end a partnership of 123 with Trott reaching a patient, 128-ball 50 not long afterwards.
But Southee bowled Bairstow with an inswinger, then got Prior for the second time in the match as the wicketkeeper pulled tamely to square-leg to bag a pair. When Kane Williamson then turned one to bowl Trott, England had foregone much of their advantage that Anderson had set up for him.
It had been Stuart Broad who had done the immediate damage for England, dismissing Black Caps captain Brendon McCullum (2) with the fourth ball of the day.
Williamson (60) held the innings together, but any hopes the tourists had of a first innings lead effectively evaporated when he was caught behind by Prior off Anderson.
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