The Andy Samberg sitcom, about a travelling American hippie who crashes into the lives of a British family, averaged 1.15m (6%) in the 10pm slot.
With Greg Davies and Tyger Drew Honey also starring, Cuckoo smashed the record set by Jack Whitehall's Bad Education only last month.
Don't Tell the Bride pulled in a strong 918k (3.9%) an hour earlier on the popular digital channel.
The Great British Bake Off's audience soared again on BBC Two, drawing a new high of 4.54m (18.8%) in the 8pm hour. Vikings followed with 1.64m (6.9%).
Capping a successful night for the corporation, BBC One's Newcastle-set period drama The Paradise premiered with 5.47m (23.1%) in the 9pm hour.
Over on ITV1, a new episode of Midsomer Murders interested just 3.99m (16.6%) between 8pm and 10pm, but added 432k (2.1%) on +1.
The Martin Lewis Money Show debuted with a respectable 3.53m (16%) on ITV1 at 7.30pm (+1: 161k/0.7%), airing opposite a highly-rated episode of EastEnders.
The Boy Who Can't Forget took 1.87m (7.9%) for Channel 4 at 9pm, adding 385k (2.3%) on timeshift. 8pm's Double Your House for Half the Money managed 1.34m (5.6%) and 211k (0.9%) an hour later.
Meanwhile, Person of Interest anchored Channel 5's night with 964k (4%) in the 9pm slot, adding 175k (1%) an hour later.
Overall, BBC One topped primetime with 23%, ahead of ITV1's 16.7% (+1: 1.3%). BBC Two claimed third place with 9.8%, beating Channel 4's 5.7% (+1: 1%), and Channel 5's 3.3% (+1: 0.3%).
BARB ratings data supplied by Attentional