The visitors came into the day looking to finish off the New Zealand first innings to get some kind of lead and they did just that in the morning session as they bowled them out for 278, which gave England a lead of 29 runs.
England then had to bat again and try and build a big lead and the are well on their way to doing that after finishing on 202-3 at the end of the day which gave them a substantial lead of 231 with seven second innings wickets remaining.
Watling and Southee frustrated the visitors early on
Day three at the Hagley Oval started with the hosts resuming their first innings on 192-6, 115 runs behind England's score of 307, with BJ Watling 77 not out the key for the home side.
Watling though had good support from Tim Southee, who decided to take the attack to the England bowlers to try and put the pressure back on them.
The pair frustrated the English bowlers until James Anderson got the new ball in his hand and he produced a fantastic delivery too break the partnership on 48 when he removed Watling for 85.
Broad completed yet another five-wicket haul for England as Southee blasted a half century for the hosts
It didn't take long for England to get their eighth wicket either as Stuart Broad took his fifth wicket of the innings to remove Ish Sodhi for one.
Southee though continued on his merry way and brought up his half century from 45 balls but was then dismissed three balls later by Anderson.
It left England needing one final wicket to finish off the innings quickly but Trent Boult and Neil Wagner has other ideas as they started to play their shots as they put on a valuable 39 runs for the final wicket.
Boult and Wagner added important runs for the hosts for the final wicket
Their partnership was finally broken by Broad as he removed Boult for 16 to bowl the hosts out for 278, which gave England a lead of 29 going into their second innings.
It meant that England had to negotiate a tricky few overs before lunch and they did just that as they ended the session seven without loss with thoughts of building a big lead after the break.
Cook failed with the bat once again
After lunch, Mark Stoneman and Alistair Cook began confidently and just as the pair looked like they could build a big partnership, Boult once again removed Cook for 14 as he has done all series to leave the score on 24-1.
It meant that Cook's dismal series with the bat finished with him averaging 5.75 which is not good enough for a man of his quality.
The wicket of Cook brought James Vince to the crease and alongside Stoneman, the pair batted throughout the remainder of the afternoon session without losing anymore wickets.
The pair took their partnership passed the half-century mark, while Vince passed his own half century as England finished the session on 113-1, with a lead of 142.
Stoneman and Vince hit half-centuries but failed to go on to make three figures again
After tea, Stoneman was next to bring up his own half century as both batsmen looked very assured at the crease.
The partnership through was finally broken on 123 when Southee removed Stoneman for 60.
The big question therefore after that was whether or not Vince could go on to make his century and that resulted in a no when he drove at wide ball from Boult to end his innings on 76.
Root and Malan saw England to the close with a lead of 231
Them two quick wickets brought Joe Root and Dawid Malan together and the pair successfully saw the visitors to the close without losing anymore wickets.
It meant that England finished the day on 202-3, with a lead of 231, with Root returning tomorrow 30 not out and Malan returning 19 not out as the visitors looked to build such a lead to level the series.