Che Adams bagged a brace as Southampton had to come from behind to secure a 2-1 Carabao Cup victory against League One Lincoln.
Top scorer Adams struck either side of half-time to spare Saints blushes after the Imps threatened an upset following Gavin Bazunu’s early own goal.
The lacklustre hosts laboured for much of a forgettable fourth-round tie at a sparsely-populated St Mary’s, leaving Jones with plenty to ponder as he plots a Premier League survival mission.
Adams’ winner – his eighth goal of the season – arrived 16 minutes from time, preventing the jeopardy of a penalty shootout, which Saints had required to sneak past third-tier Sheffield Wednesday in the previous round.
Lincoln, who sit 14th in Sky Bet League One and beat Championship Bristol City in round three, acquitted themselves well and will probably leave the south coast feeling aggrieved as replays suggested Adams’ 25th-minute equaliser was offside.
Saints substitute Samuel Edozie squandered a golden chance to make the result safe in added time when he somehow shot wide of an open goal, while match-winner Adams should have claimed a hat-trick with another excellent opening.
Jones’ maiden match as Saints manager – a 3-1 Premier League loss at Liverpool on November 12 which left the club second-bottom of the top-flight table – came two days after he replaced the sacked Ralph Hasenhuttl.
The former Luton boss was forced to wait a further 38 days for his home debut due to the World Cup and, having named a strong team, he endured a nightmare start.
Ainsley Maitland-Niles woefully sliced a Max Sanders corner high into the air inside two minutes and, as the ball dropped dangerously underneath the crossbar, Bazunu inadvertently bundled home under pressure from Imps defender Paudie O’Connor.
Jones had plenty of time to work with his new squad during the enforced break in domestic football, with Germany international Armel Bella-Kotchap and Ghana defender Mohammed Salisu the only Saints players selected for Qatar.
His disjointed side took time to bounce back from the shaky beginning and appeared to benefit from a significant slice of fortune for their equaliser.
Adams, who moments earlier was denied by a fine stop from City goalkeeper Carl Rushworth, headed home a Mohamed Elyounoussi cross but replays suggested it should have been disallowed for offside.
With VAR not being used in the competition until the semi-final stage, the goal was allowed to stand, much to the frustration of Imps boss Mark Kennedy and the healthy travelling support.
Lincoln’s only win at Southampton was a 3-2 second-tier success in December 1960.
The visitors were far from disheartened by the controversial leveller and almost regained the lead when Bazunu produced a smart stop to deny the lively Charles Vernam just before the break.
Murmurings of discontent greeted the half-time whistle and Southampton continued to toil following the restart, despite dominating possession.
City keeper Rushworth went largely untested, while Lincoln enjoyed further moments of attacking enterprise as they went in search of a shock.
With the threat of spot-kicks beginning to loom, Southampton finally went ahead.
Imps defender Joe Walsh blocked Elyounoussi’s acrobatic effort on the line following Theo Walcott’s cross but Adams was on hand to turn home the rebound.
Sanders came close to levelling with an effort from distance late on before Edozie and Adams each contrived to waste glorious chances in added time.
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