Victory made Exeter just the fourth English club to win both the Premiership and European titles in the same season following their thrilling 31-27 victory over France's Racing 92 in last week's Champions Cup final in Bristol.
Exeter led 13-10 at the break after England centre Henry Slade scored a fine solo try before Wasps hit back with one of their own through Jacob Umaga.
In an attritional second half, Exeter's pack just did enough to give fly-half Simmonds the chances he needed, including a penalty with the last kick of the game that sealed victory.
They were also missing injured New Zealand centre Malakai Fekitoa.
Wasps hit back on the half-hour through fly-half Umaga, with the nephew of New Zealand star Tana Umaga stepping off his right foot and beating three defenders from 25 metres for a try under the posts.