The cavalier right-back’s 65th minute set-piece was the decisive blow in a contest where Hibs were left to rue some glaringly missed opportunities at crucial moments, none more so than just a minute before Tavernier struck when on-loan Celtic midfielder Liam Henderson fluffed his lines horribly with the goal gaping.
While it was not their most eye-catching or cohesive display on Warburton’s watch so far, Rangers were reasonable value for their sixth straight competitive victory in as many matches.
It leaves Alan Stubbs’ men six points off the Championship pace in these embryonic stages of the campaign.
It may have been only the third league fixture of the season but there was a sense of significance enveloping the occasion in front of a sell-out crowd which suggested both teams appreciated the possibility of securing a useful psychological edge in pursuit of the title and automatic promotion.
There was a clear level of tension attached to the work of players in both blue and green, with neither able to gain a telling level of ascendancy for any sustained period in a goalless first half.
Rangers, as has been the way under Warburton so far, attempted to force themselves onto the front foot from the start. There was an early scare for Hibs when goalkeeper Mark Oxley was caught out by Fraser Fyvie’s pass back and lost the ball to Martyn Waghorn. The Rangers striker managed to cut the ball into the penalty area, where Barry McKay was unable to take advantage.
The home side threatened again in the 12th minute, McKay’s corner from the right picking out Waghorn’s impressive leap but his header sailed over the top.
Wes Foderingham then showed he was equally as unpredictable as Oxley with the ball at his feet, the Rangers ‘keeper playing an attempted clearance straight to Martin Boyle. The Hibs midfielder was only denied a simple scoring opportunity by Danny Wilson’s terrific saving tackle.
With Henderson operating just behind central striker Jason Cummings in a 4-4-1-1 formation, Hibs began to produce some neat football and looked just as likely as their hosts to make a breakthrough.
Cummings might have done better in the 21st minute when he was picked out by Danny Carmichael’s cross from the left but miscued his shot from little more than six yards out. Hibs were giving every bit as good as they got at this stage and Boyle was the next to find space among the Rangers defence, curling a right-foot shot narrowly wide of Foderingham’s right-hand post.
Rangers attempted to up the tempo in the closing stages of the first half, McKay and Lee Wallace linking smartly to slice open the Hibs defence down the left before Paul Hanlon managed to cut out the home captain’s low cross at the expense of a corner.
McKay took it, the ball breaking to Waghorn whose low shot beat Oxley but was comfortably cleared off the line by David Gray.
Hibs countered immediately, Cummings starting a slick move which saw John McGinn and Boyle stretch the Rangers defence. Boyle found Cummings inside the penalty area but the striker wastefully directed his shot straight at Foderingham.
There was a greater degree of intensity to Rangers’ play immediately after the interval and Oxley had to make a smart save low to his left to prevent Jason Holt’s scuffed shot finding its way into the corner of the net.
Hibs had to replace the injured Gray with Dylan McGeouch and found themselves hemmed into their own half for much of the first 20 minutes of the second half. Yet it was Stubbs’ men who really should have snatched the initiative just before Tavernier’s stunning breakthrough for Rangers.
Foderingham had to scramble to his right to keep out Liam Fontaine’s close- range header from a McGinn free-kick as Hibs finally re-announced themselves as an attacking force. A dreadful error from Wilson then presented Hibs with the clearest scoring chance of the afternoon yet.
The defender gifted possession to Cummings who unselfishly played the ball inside to the unmarked Henderson. With only the exposed Foderingham to beat, however, Henderson blazed his shot wildly over the top.
Rangers made the most of that let-off, punishing Hibs in dramatic fashion just a minute later. Kenny Miller’s driven cross from the left was blocked by the hand of McGeouch to concede a free-kick just outside the corner of the 18-yard box.
Tavernier stepped forward and swept home a magnificent right-foot effort which clipped the underside of the crossbar before beating Oxley all ends up.
The raucous celebrations of the home support had barely subsided when Henderson was profligate again when Carmichael provided him with a glorious chance to restore parity. This time, he completely lacked conviction as he scuffed a shot wide from around 12 yards with the Rangers backline in some disarray.
It was a far from flawless display from Warburton’s men in that regard and they can consider themselves fortunate to have kept their first clean sheet in the league this season.
But in the business of winning matches, there remains not a blot on the Rangers manager’s copybook so far.
Rangers: Foderingham, Tavernier, Kiernan, Wilson, Wallace; Holt (Shiels 68), Halliday, Law; McKay (Oduwa 60), Waghorn, Miller (Clark 83). Subs not used: Ball, Kelly, Hardie, Walsh.
Hibernian: Oxley, Gray (McGeouch 50), Hanlon, Fontaine, Stevenson; Boyle, Fyvie, McGinn, Carmichael (Malonga 77); Henderson (Stanton 89); Cummings. Subs not used: Bartley, Reguero, Dunsmore, Martin.
Referee: S McLean