The Italian duo emerged through the mist shoulder-to-shoulder with 500m remaining of the altered 180km stage in the Alps.
Having distanced his main rivals on the last and only climb of the day, Astana's Nibali was content to allow Santambrogio of Vini Fantini take a maiden win on the Giro d'Italia - and his wildcard team's first of the 96th edition of the race.
Consistent Colombian Carlos Betancur (Ag2R-La Mondiale) crossed the line in third place, nine seconds down, while Spaniard Samuel Sanchez (Euskaltel) finished fourth at 20 seconds.
Nibali is now 1min 26secs ahead of Australian Cadel Evans on GC after the veteran from BMC finished another sodden stage in sixth place, 33 seconds behind his rival.
Colombian Rigoberto Uran - the Team Sky leader following the withdrawal of sick Olympian Bradley Wiggins - finished three seconds quicker than Evans for fifth place and stays in third on GC, 2:46 down on Nibali.
Santambrogio rises to fourth on GC, 3:53 behind the maglia rosa.
Eleventh hour changes to the race profile made stage 14 longer but flatter with the cancellation of the Cat.2 climb to Sestriere replaced with a detour through the Susa valley that added 12km onto the stage while ensuring the fireworks would come down to the last and only climb of the day.
But spectators were left in the dark when the misty and wet conditions wreaked havoc with the live host broadcast TV images cut for the last 80km of the stage - and only resumed as the leading duo approached the penultimate hairpin bend of the decisive climb inside the final kilometre.
Seven riders had broken away shortly after the start in Cervere - although Spain's Egoi Martinez (Euskaltel), Dutchman Pieter Weening (Orica-GreenEdge) and American Peter Stetina (Garmin-Sharp) all crashed from the break and were subsequently caught by the peloton.
The incident left four Italians in front of the race, with Luca Paolini (Katusha), Daniele Pietropolli (Lampre), Sonny Colbrelli (Bardiani Valvole) and Matteo Trentin (Omega Pharma-Quick Step) building up a maximum lead of 10 minutes over the peloton as the relentless rain that has hampered the entire race since Naples pounded down.
Adverse conditions may have been to blame for a high-speed crash in the peloton which saw both stage four winner Enrico Battaglin (Bardiani Valvole) and Alessandro Vanotti, one of Nibali's key Astana team-mates, withdraw. Both Italians were taken to hospital, Battaglin with suspected broken ribs and Vanotti with a fractures collarbone.
During the long, flat and wet drag to the uphill finale news filtered through that the race organisers RSC had made the reluctant decision to cancel Sunday's ascents of both Mont-Cenis and the summit finish of the Col du Galibier due to heavy snow in the French Alps. There were also yet-to-be-confirmed rumours that the whole stage would be cancelled and replaced with an enforced early second rest day while RSC came up with a contingency plan.
But the remaining riders were more concerned with the task in hand - and the leading quartet arrived at Bardonecchia, at the foot of the final climb of Jafferau, with a lead of five minutes.
Trentin, a key team-mate of Britain's Mark Cavendish, was the first to fall back, and he was soon followed by Pietropolli.
Back with the maglia rosa group, Colombian Sergio Henao (Sky) and Italians Diego Rosa and Franco Pellizotti (both Androni Giocattoli) attacked with four kilometres remaining.
Former race leader Paolini was hungry for a second stage scalp in his belated maiden appearance in the Giro - but the advantage of the two leaders was coming down fast, hovering below the minute-mark inside the last two kilometres.
The Henao trio was soon caught as Nibali made his decisive attack with Santambrogio. They passed their fellow Italian escapees inside the final kilometre and then burst through the mist with 500m remaining.
Victory went to 28-year-old Santambrogio, who finished second behind Nibali in the Giro del Trentino earlier in the spring.
But Nibali - also 28 - will be happy with his day's work after mopping up bonus seconds for second place, plus taking more than 30 seconds over Evans, his principal rival.
The big loser of the day was Dutchman Robert Gesink, who crossed the line surrounded by Blanco team-mates more than four minutes in arrears to drop outside the top ten and see his hopes of a podium finish left in tatters.
The 2011 champion Michele Scarponi (Lampre-Merida) also suffered an off-day, huffing and puffing his way over the line 1:28 in arrears. The veteran Italian stays in fifth place on GC, but is now 3:53 down on Nibali with one week of racing left.
Sunday's stage 15 was set to finish atop the Col du Galibier but snow and bad weather has led to the cancellation of the final climb as well as the earlier ascent of Mont-Cenis.
A shortened parcours will still climb the Col du Telegraph but will finish at the town of Verneys after a 3km climb from Valloire - although this is yet to be confirmed with some reports suggesting the Galibier will now be climbed up to 2,300 metres.
- Sports & Recreation
- Cadel Evans