David Tennant and Olivia Colman's highly-anticipated eight-part series launched with over six million viewers in the 9pm slot.
Over 6.15 million (25.2%) tuned in for the opening instalment with an extra 716k (4.4%) switching on to watch on +1.
BBC One's similar crime series Mayday dropped to an audience of 4.3 million (17.8%) in the same time slot.
Earlier, the 1000th episode of A Question of Sport amused 4.18 million (16.5%) on BBC One at 8.30pm.
On BBC Two, University Challenge entertained 2.78 million (6%) at 8pm, while Food and Drink collected 1.97 million (6.2%) at 8.30pm. The Flying Scotsman: A Rail Romance pulled in a respectable 1.79 million (7.43 million) in a competitive 9pm slot.
Channel 4's Embarrassing Bodies was watched by 1.57 million (6.5%) at 9pm with an extra 360k on +1.
Meanwhile, Channel 5 picked up 853k (3.54%) for Robson Green's Extreme Fishing Challenge at 9pm, while Manchester United: Munich Air Crash was watched by 856k (5.23%) at 10pm.
Sky1's Arrow continues to pull in solid ratings with 560k (2.24%) sticking with the comic action series at 8pm.
BARB ratings data supplied by Attentional