Ashton Hewitt's second try of the game three minutes from time looked to be decisive in a thriller at Rodney Parade, but Ulster refused to accept defeat.
Lealiifano had the final say, the fly-half going over right at the end for a try which he was unable to convert, ensuring it was honours even to leave Ulster four points behind Conference B leaders the Scarlets.
Ulster led 27-15 with only 14 minutes to play after Craig Gilroy helped himself to a double, but three tries in the space of 11 minutes from Liam Belcher, Angus O'Brien and Hewitt turned the game in the Dragons' favour until Lealiifano struck.
Glasgow have now won 10 out of 10 in the competition after seeing off the Blues 40-16 at Scotstoun.
The runaway Conference A leaders scored six tries in a one-sided encounter and were given a big helping hand by Taufa'ao Filise, red-carded only 29 minutes in for a dangerous high tackle on George Turner.
Sam Johnson and Alex Dunbar went over in the first half, with Ruaridh Jackson, Samuela Vunisa, Leo Sarto and Nikola Matawalu scoring five-pointers in the second as the Warriors claimed another bonus-point win.
Southern Kings' wait for a first win in the competition goes on after Sam Hidalgo-Clyne came off the bench to score a second-half hat-trick in Edinburgh's 48-21 success at Nelson Mandela Bay Stadium.
Photo Getty Images. Caption: Christian Lealiifano is on loan at Ulster from Brumbies