The defeat, delivered through a first-half strike from the north-east outfit, brings an end to the side's hopes of advancing to the Round of 32.
The starting lineup saw a return to action for Ashton Scally who was making his first appearance since his senior debut on the final day of last season away to Falkirk.
As well as the action on the pitch in the north-east, those of a Rangers persuasion were keeping a close eye on results elsewhere in the competition.
The hosts had their own incentives tonight as they targeted a top six finish, and it was the League One side who threatened first when Seb Ross was slipped beyond the Gers rearguard but the offside flag was already raised before he slotted a finish under Rydnn McGuire.
Indeed, the visitors responded with an opportunity of their own when Josh Gentles, victorious with Airdrieonians in this stadium just last month, did ever so well to brush off the attentions of Danny Strachan on the left, but his curling finish from a difficult angle sailed off target.
Callum Burnside scored twice for the Diamonds that day, and he certainly looked Rangers’ brightest threat in the opening blows, albeit opportunities were few and far between.
The Balmoor outfit already had two of their players in the book before the half-hour mark with both Gentles and Burnside brought down in space just inside the opposing half.
A third caution remarkably arrived when Robel Teklemichael hauled down Kyle Glasgow, and it perhaps spoke to the cagey nature of the first-half until that point that there were more cards handed out than attempts at goal.
However, the home side broke open the scoring nine minutes prior to the interval when Rangers were caught on their heels defensively and Bobby McLuckie lashed onto the loose ball to fire beyond McGuire first-time.
The visitors sought an immediate response when Glasgow wriggled away from a pair of Peterhead defenders on the break before picking out Burnside haring forward on the left. The Northern Irishman found a shooting opportunity inside the penalty area, but after his initial effort was blocked he couldn’t quite stab the rebound beyond the goalkeeper from an acute angle.
Peterhead were grateful to their goalkeeper four minutes before the interval when the Gers looked certain to force home a leveller when Burnside was once again fed inside the penalty area. But after repelling his initial low strike from distance he sprung up to thwart the winger on the follow-up.
Scally’s evening was finished on 50 minutes when he was withdrawn for Calum Young as his minutes continue to be built up following his return to action.
Rangers required quite the turnaround to book their ticket to the Round of 32, with Luca Rankin almost finding an improbable equaliser when his corner delivery was almost taken beyond the goalkeeper and into the net by the north-east wind.
Glasgow was then audacious in his attempts to catch the goalkeeper off his line when he sprung forward on the break and spotted the opportunity, but his effort from 45 yards out was comfortably collected.
A second of the evening from Peterhead would surely kill the Gers’ hopes of advancing, and they were grateful to McGuire when he tipped Lyall Keir’s effort from the edge of the penalty area over the top.
Minutes later, a clever darting run from Burnside saw the winger flash a dangerous delivery across the face of goals, although there were no takers in Rangers colours.
Time was ticking on the away side’s journey in this competition as Gentles swivelled smartly 25 yards from goal but couldn’t quite slalom his way through a crowd of Peterhead bodies.
It was the final action of note on the evening, with the exception of a fine McGuire stop, as the referee soon blew full-time on Rangers' hopes of progressing.
RANGERS: McGuire, Patton, Kerr, Wyllie, Scally (Young, 50), Rankin, Hutton (Smith, 63), Crilly (Fergusson, 75), Glasgow (Cameron, 63), Burnside, Gentles
Subs not used: S. Reid, Owen, Ngwenya, J. Reid, Hall
PETERHEAD: Hepburn, D. Strachan, Davies-Browne, Keir, McLuckie, Stokes (Carnwath, 68), Pawlett (Yule, 58), Ross, Luyeye (Jas Brown, 79), Teklemichael (Smith, 68), Kerr
Subs not used: Newman, Megginson, R. Strachan, Jo Brown
Images: Duncan Brown