Wasps extended their lead at the top of Group Three in the Amlin Challenge Cup with the victory at Adams Park.
The hosts, who drew 13-13 in France last week, sailed into a 17-0 lead but saw Bayonne gradually claw back the deficit to just four points before Masi crossed the line to calm the home fans' nerves.
Three Stephen Jones penalties and a try from Elliott Daly put Wasps 14-0 up inside the opening half-hour, and a penalty from Daly extended their lead before Joe Rokocoko's converted try on the stroke of half-time gave Bayonne hope.
Jones and Jacques Louis Potgieter exchanged penalties early in the second half before another Potgieter penalty hauled Bayonne back to just 20-16 down with 20 minutes left on the clock.
Billy Vunipola's sin-binning in the 62nd minute threatened to cost Wasps dear but Masi's try in the 73rd minute put the hosts firmly back in command and Nicky Robinson's subsequent conversion extended their lead back to 11 points.
Robinson kicked another penalty three minutes from time to put the gloss on a fine win for Wasps, which moves them five points clear of Bayonne at the top of their group with four games played.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.