The former European Tour Rookie of the Year shot rounds of 69 and 71 in yesterday's weather-interrupted local final qualifier at Royal Cinque Ports.
He finished joint-second and faces Andrew Johnston, Simon Lilly, Alex Christie in a shoot-out at 8am this morning with two places up for grabs at Sandwich.
"I holed out a lot better than I have recently," said Henderson, who last played in the The Open at Muirfield in 2002.
After a three-hour delay due to lightning in Kent, the Scot, who had started his second round at the tenth, returned to birdie the 16th before parring his final 11 holes.
He got up and down from a bunker at the seventh then holed from three feet at the ninth to secure his place in the play-off.
At Prince's, where just three places were up for grabs as well, Hayston's Stephen Gray missed out by a single shot after rounds of 68 and 72.
Recent St Andrews Links Trophy winner Tom Lewis led the qualifiers at Rye, where Elliot Saltman followed an opening 69 with a 66 but fell two shots short of a play-off.
Former US Open champion Michael Campbell also missed out after rounds of 68 and 72 for a four-under-par total at Prince's.