Mulligan, who completed a move to Scunthorpe from Doncaster on Thursday, was instrumental as the Kiwi side held a side 39 places above them in the FIFA rankings to a stalemate in Tallinn - Estonia's capital.
He set up their equalising goal, playing a free-kick into the box for captain Danny Hay to fire home after the eastern Europeans had taken the lead in the game in Switzerland.
Estonia had opened the scoring after three minutes when Ragnat Klavan outpaced the visiting defence before firing Ross Nicholson.
But he is in for a tough time next week when he lines up against Brazil, who are completing their preparations for their defence of the World Cup - which kicks-off four days later in Germany.
All Whites coach Ricki Herbert is confident his side, who did not qualify for the World Cup, can do themselves justice against the best side on the planet.
He said: "We've proven we are competitive with those teams ranked in the top 70, so who knows.
"Brazil can beat anyone at any time, by any score, so we've just got to go and do the best we can.
"We don't want to get hammered, but it can happen. It is a massive step for us - we're taking on the World Cup favourites.
"It is one of the biggest events in the world, so it's just nice to be on the same pitch."