Rangers strolled to victory in the first game of their defence of the SPL title they won last season.
Dado Prso put the champions ahead midway through the first half, sliding in to net the rebound after Alex Rae's volley was parried by Roddy McKenzie.
Their second goal came after 53 minutes when Jose Pierre-Fanfan prodded in Peter Lovenkrands' deflected cross.
The Dane scored a third in injury time with a low strike from 18 yards after Livi's Richard Brittain was sent off.
Rangers dominated possession in the early stages, but it was 12 minutes before they managed an effort on goal - Barry Ferguson dragging a shot wide.
Livingston replied with a long-range drive by Dubi Tesevic that Ronald Waterreus ushered behind.
Rangers' pressure finally paid off after 23 minutes.
The ball was cleared by Livingston to Rae, who thundered in a volley from 25 yards that McKenzie did well to keep out.
But Prso was first to react inside the box and he side-footed the ball high into the net.
Nacho Novo could have doubled the lead almost immediately, but he just failed to connect with an excellent Lovenkrands' cross.
Thomas Buffel should have opened his goalscoring account for the season in the final minute of the first half, but he blasted over after Ferguson had played him in on goal.
The procession towards the visitors' goal continued after the interval and Prso should have hit the target when the ball fell kindly for him 12 yards out, but he sliced his shot wide.
Jose Pierre-Fanfan (left) celebrates his debut goal
It was no surprise when Rangers finally got a second goal. Lovenkrands' cross was deflected towards his own goal by Manu Dorado and Pierre-Fanfan helped it over the line.
Shortly afterwards, McKenzie came off his line to deny Novo a third.
Lovenkrands, who was performing well in flashes, rising to the challenge laid down to him by manager Alex McLeish, almost got on the scoresheet after 65 minutes following a wonderful run that took him into the box, but his shot was blocked by the leg of McKenzie.
Livi's task was made all the more difficult when Brittain was shown a straight red card for a late challenge on Ian Murray with 16 minutes remaining.
Nonetheless, Waterreus had to be alert to turn a long-range drive by Livi sub Scott McLaughlin round the post.
Steven Thompson, on for Prso, should have added to his side's tally, but he shot straight at McKenzie with only the keeper to beat.
Lovenkrands scored the goal his performance deserved in added-on time, a low drive from just inside the box after he had beaten two defenders.
Rangers: Waterreus, Ricksen, Andrews, Pierre-Fanfan, Murray, Novo (Adam 85), Ferguson, Alex Rae, Lovenkrands, Buffel (McCormack 70), Prso (Thompson 63).
Subs Not Used: Klos, Malcolm, Burke, Smith.
Goals: Prso 23, Pierre-Fanfan 53, Lovenkrands 90.
Livingston: McKenzie, Mackay, Tierney, Dorado, Pinxten, Walker (McLaughlin 68), Adams, Tesevic, Brittain, Scott (Pereira 57), McPake (Snodgrass 57).
Subs Not Used: Roy, Strong, Adam, Dorrans.
Sent Off: Brittain (74).
Booked: Walker, Pereira.
Ref: C Thomson