Smith's New Zealand Bow Out
Both teams had opportunities to create chances but were lacking invention in the final third and looked tired all over the pitch.
Roque Santa Cruz was an occasional exception for Paraguay, creating their best chance of the half by floating out to the right wing and chipping a ball into the path of Denis Caniza, who hit a vicious half-volley wide of the right-hand post.
Caniza at least helped Paraguay come out as the statistical victors of the first half by hitting around five shots towards Mark Paston's goal, even if they all ended up in a similar position amongst the sleeping fans.
New Zealand at least created some half-chances for themselves in the second period, the kind that need to be taken if a team has intentions on getting further in the World Cup.
Simon Elliott, whose free-kicks were the most likely source if a goal for a team lacking creativity, was found in space on the edge of the box three minutes into the half, but he could only find the stanchion behind the goal.
A Shane Smeltz header in the 84th minute was the next chance the All Whites could muster, but that flew well wide and Chris Wood couldn't stretch far enough to reach Smeltz's deep cross five minutes later, although he had been flagged offside.
Paraguay grew as the second half went on and, while they were always going to be happy with a draw, began to show touches of ability.
Only goalkeeper Paston saved New Zealand, first from a Cristian Riveros header after an hour, then with 15 minutes to go by parrying Edgar Benitez's shot then flicking the rebound away from the onrushing Lucas Barrios.
Paraguay didn't show enough invention to earn more than a point, while New Zealand can go home proud at having not lost a match at the World Cup.