Tim Southee on Saturday picked six wickets to put England on the back foot but opening batsman Burns hit a ton to make sure the hosts were still in the game.
England was bundled out for 275 as Burns (132) ran out of partners on Saturday. Four England batsmen scored ducks as New Zealand dismantled the Engish batting order on day four.
Laxman also praised Devon Conway for his "outstanding" double on his Test debut against England.
"Openers from both teams being the tenth man dismissed. Must be some sort of a record. Devon Conway was outstanding on his way to a debut double hundred for NZ and Rory Burns century has ensured England are not totally out of the game," Laxman tweeted.
After gaining a lead of 103 runs, New Zealand openers Latham and Devon Conway saw out the new ball. While the run-scoring was slow, both players kept the England bowlers at bay.
The openers put on 39 runs for the first wicket and England finally got the breakthrough in the 19th over of the second innings as Ollie Robinson clean bowled Conway (23).
Skipper Kane Williamson (1) failed to leave the mark with the bat as he was adjudged leg-before wicket on a ball bowled by Robinson.
Nightwatchman Neil Wagner next came out to the middle and along with Latham, he ensured that New Zealand reach stumps with eight wickets in hand.
London, June 6
Former Indian batsman VVS Laxman feels Rory Burns' gutsy ton has ensured England is not otally out of the first Test against New Zealand.
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