Annan showed flashes of attacking intent throughout the 90 minutes and they should have made it 1-1 before the hour mark when ref Paul Robertson awarded a penalty and sent Lee Wallace off for a push on Jack Steel, denying the player a goalscoring opportunity.
Scott Chaplain stepped up but Neil Alexander was there to make a crucial stop.
Rangers, however, continued to show their fighting spirit with Little and Templeton adding two more excellent goals.
Charles Green walked out onto the pitch before kick-off to thank fans after it had been announced £22.2million had been raised from the club’s IPO and trading in the shares starts tomorrow when the market opens at 8am.
This produced a warm applause from the Ibrox faithful on what was a cold night in Glasgow’s south side.
Ally McCoist made two changes to his starting eleven for this evening’s clash with Fran Sandaza and Barrie McKay returning in place of the injured Dean Shiels and Kevin Kyle.
McKay made a difference when he went on against Montrose on Saturday and he looked up for it again from the first whistle against the Galabankies.
After just four minutes he sped away from his marker down the left wing and his cross was palmed away by Alex Mitchell.
The ball went straight to Sandaza but with the keeper grounded the Spaniard’s sclaffed shot from 10 yards went wide.
On 8 minutes McKay again found space down the left but instead of shooting, which was the better option, he elected to cut it back to Little and his effort was blocked.
It was wave after wave of attack and next up to try his luck was Templeton who blasted a long ranger over the bar into the Broomloan Stand.
The Gers winger, wearing the number 10 jersey, then sent a dipping effort towards goal from 25 yards but Mitchell was there again to make a stunning fingertip stop.
With 20 minutes played it was remarkable Rangers hadn’t opened the scoring but on 24 minutes the stadium was almost silenced when former Ibrox kid Chris Jardine, who played in the youth ranks with Barry Ferguson, found space in the box but his low shot brought out the first save of the match from Alexander.
Before the half hour mark the Light Blues finally got the goal their play deserved.
Templeton picked the ball up from 20 yards out and his low, drilled shot dipped and swerved before beating Mitchell at his near post.
Rangers continued to dominate the match up until the break and Macleod came close to doubling his side’s advantage late on when he headed Little’s cross over the bar after making a good run into the box.
But with just one goal separating the sides Annan were still in this game as they reappeared for the start of the second period.
And on 49 minutes Ally Love’s free kick had to be watched by Alexander as it flew over albeit it was never going to trouble the Gers number one.
Chaplain then let fly with another ambitious effort from 25 yards but the outcome was the same.
On 57 minutes Wallace was then adjudged to have pushed Steel when challenging for a deep cross into the box.
The ref immediately pointed to the spot, sent off the left back and booked McCulloch after the skipper had said a few words in his ear.
Chaplain looked confident as he sprinted up to the ball but his low shot lacked the power and accuracy to beat Alexander who dived to his right to make the initial stop before grabbing the ball at the second attempt.
What a crucial save it proved to be because within five minutes his side had scored a second and it was a cracker from Little.
The Ulsterman burst clear down the right and with the Annan defenders struggling to match his pace he unleashed a great right foot drive which across Mitchell into the opposite bottom corner of his net.
Even up against ten men Annan now had a hill to climb and on 69 minutes it became a mountain when Templeton made it 3-0.
After jinking his way past a defender he sent a curling effort into the net from 20 yards and it capped an excellent performance from the man of the match.
Both Fraser Aird and Kal Naismith were given the chance to stretch their legs but by the time they went on the game was already over after their teammates had shown great resilience to claim three more points.
RANGERS: Alexander; Argyriou, Hegarty, McCulloch, Wallace; McKay (Aird 75), Hutton, Macleod, Templeton; Little (Naismith 85), Sandaza (Perry 58)
SUBS: Currie, Crawford
Attn: 42,135