Root (105no) and Michael Carberry (77) shared a stand of 182 in a stumps total of 219 for two as the captain, sure to be named in England's Test squad, took his first-class tally well beyond 500 runs in just those four attempts so far this summer.
Toby Roland-Jones (four for 54) had earlier doubled his wicket tally to help bowl the Kiwis out for 285 - a mediocre return for the tourists, who had closed a rain-restricted first day on 184 for three but endured a bleak second with both bat and ball.
After Hamish Rutherford went early, for the addition of only 10 to his overnight 116, the Kiwis never threatened significant consolidation despite a durable 42 not out from Dean Brownlie.
Root and Carberry, joining forces after the early departure of Varun Chopra on another mostly cloudy and occasionally rainy day, have fared well together previously for the Lions. Almost exactly a year ago, they put on 197 in a 10-wicket win over West Indies at Northampton.
This time, apart from an escape for Root on 23 when Brendon McCullum dropped a tough chance high to his right at second slip off Doug Bracewell and then another close call for lbw when Trent Boult found some late inswing, the second-wicket pair always looked in control. That was far from the case for the New Zealand batsmen, once Rutherford had gone run out when he tried to steal a single off Graham Onions but did not bargain for a direct hit from Chris Woakes.
It was the first of two big wickets to fall for one run, Kiwi captain McCullum's first innings on tour lasting only four balls before he poked Onions to gully. Brownlie and BJ Watling kept the Lions at bay for the next 11 overs until a little variable bounce from the Bennett End saw the wicketkeeper edge an attempted back-foot force at Woakes down on to middle-stump.
Tim Southee's short innings was then typically eventful, including a pull high over square-leg to get off the mark with a six and then two escapes off the bowling of his one-time Essex team-mate Ravi Bopara.
Southee did manage a breakthrough at the pavilion end, finding enough movement for Chopra to edge low to McCullum at second slip.But Root and Carberry closed out the middle session and then, between the evening showers, duly posted twin 50s.
Carberry's came first, from 117 balls, but Root's was quicker and completed impressively with a straight six after advancing to Martin's left-arm spin. They became ever more authoritative until Carberry picked out deep square-leg off Martin to end his 187-ball stay. Root completed his hundred with a cut off Martin for his 15th four.