Fresh from signing a new five-year contract earlier in the day, the Northern Ireland midfielder struck twice late in the first half of a tame friendly at Bloomfield Road on Tuesday night.
Ally McCoist's men, who begin their Scottish title defence against Hearts on Saturday, were clearly much sharper than a Blackpool side playing for the first time since their heartbreaking relegation from the Premier League.
The Seasiders are also still coming to terms with the loss of their dynamic midfield combination of Charlie Adam and David Vaughan, and so lacked bite.
Ian Holloway hopes to start filling that gap by bringing in former Rangers captain Barry Ferguson, who was thought to be watching both his old and potential new employers from the stands.
The game lacked intensity and any cohesion it had was lost amid a multitude of confusing substitutions that baffled the PA announcer in the second half.
There actually appeared to be more action off the field than on it in a quiet opening 30 minutes.
Hundreds of Rangers' sizeable following had obtained tickets in home sections and there was a long procession as police and stewards moved them to the largely vacant East Stand.
On the pitch the Scottish champions dominated possession but initially struggled to break down a Tangerines' defence in which new signing Matt Hill looked composed.
Rangers had their first opportunity after Steven Naismith was fouled on the edge of the area by Ian Evatt but Nikica Jelavic's free-kick was deflected wide.
Another new Blackpool signing, the former Manchester United trainee Bojan Djordjic, who also had a spell with Rangers, attempted some speculative passes but there was little goalmouth action.
Jelavic tried to engineer his own opportunity as he flicked the ball up in the area but miskicked his overhead volley.
Jelavic then enjoyed some luck as the ball rebounded into his path as he charged into the area but Naismith could not convert his ball in.
Gary Taylor-Fletcher, whose Blackpool future is uncertain, had the hosts' first serious chance with a chip to the back post but Allan McGregor tipped over.
Rangers went ahead 10 minutes before the interval as they broke from a Blackpool corner.
Juan Manuel Ortiz, the club's only summer signing to date, found space down the right and crossed to the far post for Davis to jump and volley home.
Davis then doubled his tally four minutes later with a fine solo effort, skipping around two defenders and firing a low shot past Matt Gilks from six yards.
Holloway made 10 changes at half-time while Davis left the action for Rangers.
McCoist made four more substitutions 11 minutes later, including the introduction of James Beattie, who ended last season on loan at Blackpool.
Another of the Seasiders' new faces, Gerardo Bruna, signed from Liverpool yesterday, almost made an immediate impression as he curled a 65th-minute free-kick against the post from 25 yards.
Striker DJ Campbell, who has been linked to West Ham, Aston Villa, Fulham and QPR, then fired another chance over.
Yet while the game petered out, the passion of Rangers' support was clearly evident and they will look forward to the weekend in good heart.