The Miranda Hart show pulled in 9.04 million (32.5%) at 9pm and Brendan O'Carroll's Irish comedy amused 8.1m (29.8%), down slightly on their highly-rated Boxing Day outings.
The BBC One studio sitcoms achieved almost triple the audience of ITV's music special Gary Barlow and Friends, which attracted 3.03m (11.3%) between 9pm and 10.15pm and 460,000 on +1.
BBC Two's showing of Nature's Weirdest Events (2.96m/10.7%) helped it gain an unexpected 8pm lead over Celebrity Who Wants to Be a Millionaire? (2.92m/10.5%) on ITV1 (+1: 253k).
Queen Victoria's Children, BBC Two's 9pm documentary, managed a decent 2.44m (8.8%) before Charlie Brooker's 2012 Wipe picked up 1.29m (6.2%).
Earlier in the evening, Disney's family film Up made its terrestrial premiere on BBC One with 7.19m (27.5%), securing a big primetime win for the channel.
Overall, BBC One's average of 29.2% was nearly triple ITV's 10.3% (+1: 1.2%) across primetime, while BBC Two beat Channel 4 to third place with 7.8% versus 7.3% (+1: 0.6%). Five followed with 6.1% (+1: 0.4%).
On the multichannels, Sky Sports 1's darts coverage averaged 1.2m (4.7%) between 8pm and 11pm.
BARB ratings data supplied by Attentional