New Zealand A, who resumed on 187 for 4, were already 261 runs in front after England's collapse to a dismal 107 on the second day.
And Harris and Howell, 31 and 51 respectively overnight, continued to prosper despite the occasional unsettling delivery from seamers Chris Silverwood and Andy Caddick.
Silverwood's first ball of the day, to Howell, went through the top of the pitch and struck the batsman on the body as he tried to duck out of the way. But after half-an-hour's play New Zealand A had gone on to 214 for 4, a lead of 288, with Howell on 63 and Harris on 45.
Spinners Robert Croft and Phil Tufnell took over from pacemen Silverwood and Caddick and the Middlesex slow left-armer Tufnell finally dismissed Howell lbw for 66.
Howell and Harris had added 117 for the fifth wicket, but that was England's only success in the first half of the morning session. Jason Mills came in to join Harris, who went to his half-century.
The timing of this game has not helped England, with just one travel day in between the torture of the final afternoon of the Auckland Test and the start of this four-dayer. A sporty pitch has also proved a disincentive.
The decision to play all five of the players who did not play at Auckland has given England a weakened side, with the presence of only four front- line batsmen.
England's players seemed to lose some of their enthusiasm for the fray as if they were going through the motions before next week's Test and then the Christchurch Test which follows it. Tempers were even shortening towards the end of the second day, especially when several appeals were turned down.
Their lack of interest seemed to increase the moment that Geoff Allott and Heath Davis emerged to bowl with as much, if not more, hostility than on the first evening and any hopes of a first-innings lead soon disappeared as the pair bowled explosively when England resumed on 30 for 3.
Both harbour ambitions of making the second Test in Wellington, and the variation offered by Allott's bustling left-armers might just swing the vote his way.
Davis, meanwhile, is a far better bowler than he was when he toured England back in 1994 and took 1 for 93 in 21 overs at Trent Bridge, a game which remains his only Test.
The ball which claimed Nasser Hussain, a rapid lifter from just short of a length, was as close to being unplayable as makes no difference.
Davis had taken three wickets in 12 balls and when he rested his overall figures were an impressive 4 for 22 from 14 overs. His partner in destruction, the 25-year-old Allott, finished with 4 for 44.
John Emburey, the England assistant coach, looked on the bright side of a disappointing second day. "It's more important in these games for the players on the fringe of the Test team - like Chris Silverwood, Robert Croft and Ronnie Irani, to get the opportunities of cricket in case they are selected for the next Test," he said.
"It has not been ideal having to start this game after just one day off following the first Test but we agreed to this itinerary so we just have to get on with it."
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