Broad had a hard Ashes series, taking just 11 wickets from five matches at an average of 47, and his lack of incision led to former England captain Michael Vaughan calling for him to be dropped for the fourth Test at the MCG.
Livingstone, the only change from England's Ashes squad for this tour, at least showed real promise and says he would not be overawed if called upon in this series.
Before the tour Livingstone, who played two T20Is against South Africa previous year, told ESPNcricinfo he was more comfortable as a first-class player.
It would probably take an injury for him to come into contention for either Test, so he is keen just to soak up as much experience as he can over the next few weeks.
The opening two-day warm-up match between England and New Zealand XI is slated to be held at Hamilton on Wednesday.
The teams will play a second practice match at Seddon Park, on Friday and Saturday, this time with a red ball and more orthodox playing hours.
Only when Livingstone aimed a wild drive in keeping with the day's indiscipline in the first over after "dinner" at Nathan Smith and edging through to Tom Blundell seeking to rush to his hundred did he let himself down. "But a few of us have got what we wanted out of the day".
And Vince's ability to get out when seemingly well set struck again when he was first caught behind attempting to leave the ball and then harshly given out lbw to a full toss in his second failure of the day.
Graham Thorpe, the batting coach, felt the first two sessions - in which they lost six and five wickets respectively - were "indifferent for us", which...
"But Liam Livingstone played very well". He's been given an opportunity here and has fitted in very well.
As for Livingstone, Thorpe said: "In a way people may say he's not in the potential starting XI but he's proved today, busy at the crease, intent, and shown the coaches what he's capable of". His innings is also a kick up the backside for the other players'.