Although the home side slackened off a touch after the restart, Dean Shiels made sure of the points in the closing stages as Gers edged towards two months of constant winning.
They now find themselves a dozen points clear of second-placed Elgin, having played drawn level with them on 16 games played.
Third-top Queen’s Park have two additional fixtures to play and four points behind City at present, they could yet emerge as the Ibrox side’s main challengers.
But Ally McCoist’s men visit the Spiders on Saturday and if they can win in front of a huge travelling support it will only strengthen their bid to win the title further.
This was a match in which Rangers took a relatively early lead, extended it before the break and never looked like being caught again despite rarely moving out of second gear.
Boss McCoist made just one change to the team which ultimately won well at Elgin on Saturday, with Ross Perry replacing Greek injury victim Anestis Argyriou.
And as it set out with the same attacking threats as the weekend, another thronging crowd Ibrox filtered into Ibrox expecting a strong start from their side.
What it saw instead was a static show at first as Gers took time to feel their way into the contest.
Captain Lee McCulloch did his best to rouse both the team and support with a thunderous angled drive that Jamie Barclay did well to tip over.
From the resulting corner, Lewis Macleod found Emilson Cribari but the defender’s shot on the turn lacked pace and was comfortably gathered.
Rangers were slowly finding their rhythm and a lovely reserve pass from Barrie McKay picked out Macleod, whose ball across goal was very nearly turned in by McCulloch.
Moments later, a well-worked move involving McKay and McCulloch culminated with the latter laying off for Templeton and he was on target but denied by a decent save.
Clyde looked fairly confident when they came forward but they were frequently guilty of playing wasteful passes in the final third.
And it was only a matter of time before the hosts went in front, with Wallace breaking the deadlock in fine style after 20 minutes.
With McCulloch claiming for a free kick after a couple of late touches on him, the left-back linked up well the Templeton.
A smart overhead pass then released the former Hearts defender and he slid home a cool finish under Barclay for his fourth goal of the season.
It wasn’t long after then that Andy Little’s game ended prematurely as he came off with a knee injury and was replaced by the returning Shiels.
All taking one Northern Ireland international off for another did was ensure the Light Blues continued to dominate.
And after a Kyle Hutton piledriver whistled past and Templeton shot into Barclay’s arms, they doubled their lead with a really special strike.
It was those two players who were involved, with the midfielder playing in to the former Jambo.
Templeton then bamboozled his marker with a terrific turn that left him rooted to the spot before curling a glorious 20-yard right-footed effort into the top corner.
That was the 23-year-old’s fourth goal in five starts since he returned from ankle ligament damage and he’s someone in great form for McCoist’s team at present.
McCulloch thought he had added a third shortly before the break but he was flagged offside, probably correctly.
Had it been allowed to stand, it would only have highlighted how in command the men from Govan were at the midway point.
For all that, they started the second period slowly and were certainly guilty of easing the pressure on their opponents.
Thankfully they weren’t to pay for it at a time when Clyde pulling one back might just have turned the game back into a contest again.
Hutton and Macleod both forced Barclay into action as Rangers turned the screw again but neither could follow up their goals in Elgin four days ago with more.
McCulloch should also have done better after McKay swung in from the right but he didn’t connect with the cross.
Where they all failed, Shiels finally succeeded as he turned and fired home after being played in by McKay 14 minutes from the end.
At last the points were safe and now attentions turn to Hampden, where Rangers will try to take their winning sequence into double figures on Saturday.
RANGERS: Alexander; Hegarty, Perry, Cribari (Cole 78), Wallace; Little (Shiels 25), Hutton, Macleod, McKay; Templeton (Crawford 83); McCulloch.
SUBS: Currie, Sandaza.
GOALS: Wallace 20, Templeton 38, Shiels 76.
CLYDE: Barclay, Kane, Brown, Gray, Lamie, Hay (Neil 81), Fitzharris (Sweeney 72), Scullion, Watt, Gilfillan (McLuskey 86), McColm.
SUBS: Rajovic, Oliver.
REFEREE: Crawford Allan.
ATTENDANCE: 47,463.
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