The Hampshire part-timers were on the verge of causing the day's big shock when they led through Dorian Dervite's own goal but debt-ridden Championship side Bolton levelled three minutes from time through Darren Pratley to set up a replay.
On a day of 25 ties, holders Arsenal, bidding to become the first club to win the trophy three times in succession since Blackburn Rovers in the 19th century, came from goal down to beat Premier League strugglers Sunderland 3-1.
Manchester City and Everton also made it through to the fourth round, City winning 3-0 at Norwich City in one of four all top-flight clashes and Everton ending the hopes of fourth- tier Dagenham and Redbridge with a 2-0 win at Goodison Park.
League two (fourth tier) Wycombe Wanderers made sure their name will be in the hat for the fourth round with a 1-1 draw at home to the Premier League's bottom club Aston Villa who have now gone 16 matches without a win.
Hartlepool, also representing the fourth tier, took the lead against former English champions Derby County but lost 2-1 while Portsmouth, FA Cup winners in 2008 but now floundering in League Two, earned a 2-2 draw at Championship club Ipswich Town.
Watford beat Premier League rivals Newcastle United 1-0, Crystal Palace overcame Southampton 2-1 and West Ham United edged past Wolverhampton Wanderers 1-0 at Upton Park.
Premier League West Bromwich Albion needed a last-minute equaliser to steal a 2-2 draw at home to Championship side Bristol City.
Manchester United host Sheffield United in the late kickoff.
Original source: Eastleigh denied, Arsenal progress