When stumps were drawn, New Zealand were 257 for eight in their second innings, leading by 18 runs with only two wickets in hand and a full day to play in Port of Spain.
Watling was unbeaten on 38 with Craig 29 not out after the pair had come together after tea with New Zealand, 1-0 up in the series, still 27 runs short of making West Indies bat a second time.
“We toiled hard and knew that New Zealand would make us toil hard,” West Indies head coach Ottis Gibson said. “They’ve always been that sort of a team. We never thought it was going to be easy but I am proud of the way my guys stuck in today.
“I think at the back-end there (late in the day), you could see a little bit of turn there so probably a little bit of frustration creeping in but, overall, we have had a pretty good day.”
Resuming on 73 for one, New Zealand began the day cautiously, adding just 21 runs before the first drinks break and losing opener Tom Latham for 36, caught by Kraigg Brathwaite at silly point off the bowling of left-arm spinner Sulieman Benn.
Kane Williamson reached his half-century off a painstakingly slow 166 balls before he edged paceman Kemar Roach to wicketkeeper Denesh Ramdin for 52.
Benn then took a sharp return catch to remove Jimmy Neesham for seven to leave the Kiwis reeling on 121 for four at lunch before West Indies captured two more scalps in the middle session.
Ross Taylor departed for 36 when he got a thick edge behind off medium pacer Shannon Gabriel then Hamish Rutherford, who went in at seven after a stomach bug prevented him from opening the innings, fell for 13, trapped leg before wicket by Jerome Taylor.
West Indies looked to be heading for an innings victory when Roach dismissed Ish Sodhi for 14 and Tim Southee for 15 before Watling and Craig knuckled down and survived through to stumps.
The third and final test in Barbados starts next Thursday.
“We obviously would have liked some big scores and made the second innings our first innings but that wasn’t to be,” said Williamson.
“But hopefully the two boys out there can kick on a bit tomorrow and make it either an awkward chase or bat on a bit longer and put us in a better position.”
(Reporting by Julian Linden and Mark Lamport-Stokes; Editing by Tony Jimenez/Ian Ransom)