Monye just won the scramble to touch down for the opening try
The Lions maintained their 100% record but limped into Saturday's first Test against the Springboks after surviving a battering from the Southern Kings in Port Elizabeth.
Prop Euan Murray and fly-half James Hook both departed injured inside the first 12 minutes of a first half of juddering hits that ended 3-3.
Ronan O'Gara's second penalty and conversion of Ugo Monye's fortuitous try eased the Lions' nerves, and a penalty try with 11 minutes left settled the outcome.
Kings flanker Mpho Mbiyozo did stretch over late on to the delight of a partisan crowd of 35,853, the biggest of the tour so far, but the Lions completed a hard-earned victory without further alarm.
Their sixth and final warm-up win before the Test series was far from comfortable, but ultimately those likely to miss out on the first clash in Durban did their job in difficult circumstances.
Monye disappointed with Kings tactics
It is debateable whether any of them did enough to force their way into the Test side, although Monye, a late call-up to the starting side for the unwell Shane Williams, remains favourite for the left-wing role.
The Lions' resources were already stretched in certain positions coming into this game, and their body count threatened to be diminished at almost every collision in the opening quarter.
Centre Gordon D'Arcy, starting his first game of the tour, was on the end of the first in a series of late or high tackles as early as the third minute with a welcome-to-Port-Elizabeth effort from Frikkie Welsh.
Riki Flutey and Joe Worsley also felt the full force of the Kings' overtly physical approach, fly-half Jaco van der Westhuyzen being sent to the sin-bin in the 18th minute for his hit on Flutey.
The Lions were already two casualties down by then, tight-head Murray departing with an ankle injury after just seven minutes and Hook following five minutes later after a lengthy period of treatment for a neck problem.
The incisive break that preceded was promising, but the tourists struggled to gain a foothold in the match after falling behind to Van der Westhuyzen's first-minute penalty.
Mike Blair took a quick free-kick but his intended pass to Luke Fitzgerald went straight into touch, while Monye, Ross Ford and captain Donncha O'Callaghan all dropped off tackles as the Kings enjoyed all the early pressure.
The Lions struggled at the line-out, and were smashed repeatedly at the breakdown, conceding turnovers in a manner which hardly bodes well ahead of the Test series.
Full-back Keith Earls, who has had an unconvincing tour so far, did show glimpses of the attacking potential that persuaded Ian McGeechan to include him in the squad, and his scything break from deep in the 24th minute should have led to a score.
But after swerving away from three players the 21-year-old opted to wait for support rather than go for the line, and his looping pass to Fitzgerald fell forward.
Jones expected tough Kings battle
The Lions did finally get on the scoreboard when O'Gara - on for Hook - banged over a straightforward penalty after 27 minutes, but they continued to struggle until the interval.
Worsley required treatment after a ridiculous late hit from wing Wylie Human, while Van der Westhuyzen was short with one penalty and pushed another wide before half-time.
The Lions also survived a major let-off in the 35th minute when wing Human surged into the Lions 22 and stepped inside Monye, only for O'Gara to make a crucial last-ditch tackle.
The gale blowing in off the Indian Ocean continued to howl around the upper reaches of the brand-new Nelson Mandela Bay Stadium, but the crowd created a party atmosphere in the second half.
Full-back Earls (left) had some lively moments for the Lions
Down at pitch level the Kings' early fury appeared to subside somewhat as the Lions finally established some control up front.
The line-out improved with Nathan Hines and Worsley both claiming a couple of takes apiece, and gradually the tourists found some cohesion.
O'Gara landed a superb penalty from 40m after 45 minutes, and 10 minutes later his cross-kick to the right corner led to the opening try.
Kings left wing Matthew Turner made a hash of trying to collect the bouncing ball, allowing Monye to dive around him and touch down for his fourth try of the tour, drawing level with Tommy Bowe as the Lions' leading scorer.
O'Gara's conversion gave the Lions a 10-point cushion and after replacements Matthew Rees and Shane Williams joined the fray, they earned a second in the 69th minute through their dominant scrum.
Referee Nigel Owens awarded a penalty try after replacement Kings scrum-half Josh Fowles illegally came round to disrupt it on the Lions side, and O'Gara's conversion made it 20-3.
Van der Westhuyzen's break-out with seven minutes left was halted initially by superb tackles from Worsley and O'Callaghan.
But the Kings kept coming and Mbiyozo stretched through Hines and Blair to score a rapturously-received try.
The hosts continued to pound the Lions line as the clock ticked down, but the visitors held firm.
Southern Kings: Tiger Mangweni; Wylie Human, Frikkie Welsh, De Wet Barry, Matthew Turner; Jaco van der Westhuyzen, Francois Hourgaard; Jaco Engels, Derick Kuun (capt), Ruan Vermeulen, Ross Skeate, Marco Wentzel, Solly Tyibilika, Mpho Mbiyozo, Darron Nell.
Replacements: Delarey du Preez, Dean Greyling, Lungelo Payi, Dries van Schalkwyk, Josh Fowles (for Hougaard, 42), Bevin Fortuin, Mzwandile Stick (on for Human, 55).
Lions: Keith Earls; Ugo Monye, Riki Flutey, Gordon D'Arcy, Luke Fitzgerald; James Hook, Mike Blair; Andrew Sheridan, Ross Ford, Euan Murray, Simon Shaw, Donncha O'Callaghan, Nathan Hines, Joe Worsley, Andy Powell.
Replacements: Matthew Rees (for Ford, 64), Adam Jones (for Murray, 7), Tom Croft, David Wallace, Harry Ellis, Ronan O'Gara (for Hook, 12), Shane Williams (for Monye, 64)
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