Sam Vesty’s first try of the season had brought Tigers to within three points of the hosts with four minutes of the half remaining.
But two late penalties from Danny Cipriani, one from inside his own half with the last kick of the first-half, extended the Wasps lead to nine points at the break.
The game began at a breathless pace and Tigers raced into a fifth-minute lead when Scott Hamilton fended off Mark Robinson to cross unopposed.
Wasps hit back through tries by Serge Betsen and Chris Bishay while both sides were reduced to 14-men when Alesana Tuilagi and Daniel Leo were yellow-carded for touchline incident.
Tuilagi was making his return to the team from a knee injury while Louis Deacon made his first start of the season in the second row after recovering from a back injury. Vesty made his first Guinness Premiership start of the campaign at fly-half and Aaron Mauger captained the team from centre. Marcos Ayerza, who has been out for nine weeks with a wrist problem, was named among the replacements.