Conference sides Chester and Dover upset League Two opposition to earn a place in the FA Cup second round.
Elsewhere, Byron Harrison's hat-trick helped League Two side Cheltenham win 5-0 against a 10-man Swindon side who are third in League One.
Cambridge United, of League Two, also caused an upset by beating League One opponents Fleetwood Town 1-0.
Kwesi Appiah scored after Fleetwood striker Jamie Proctor had been sent off for raising his arms in a goalmouth melee.
Eastleigh, meanwhile, reached the second round for the first time, beating Conference rivals Lincoln City 2-1 thanks to a late goal from Ben Strevens.
Richard Hill's side go into Monday's draw, which will be live on BBC Two and BBC Radio 5 live at 19:00 GMT, with live text commentary on the BBC Sport website.
They will be joined by Steve Burr's Chester, who were playing in the first round for the first time since the club reformed in 2010, and who went ahead with a fifth-minute header from full-back Ben Heneghan, with Barry Corr equalising from the penalty spot before a driven winner from Mahon, who became a father to twins on Friday.
But there was late disappointment for Conference South side Hemel Hempstead Town, who led early on at Bury - 61 places higher on the league ladder - and were minutes from a replay until Nathan Cameron and Daniel Nardiello sealed a 3-1 win for the League Two side.
East Thurrock United, of the Ryman Premier, were also eliminated, losing 2-0 at Hartlepool who are bottom of League Two.
|Burr works his FA Cup magic|
|Chester manager Steve Burr led Kidderminster Harriers to the third round of the FA Cup last season. He was sacked three days after Harriers drew with League One side Peterborough United. Harriers went on to win the replay, before going out in the fourth round at Premier League side Sunderland.|
John Akinde gave Conference Premier leaders Barnet a third-minute advantage at home to Wycombe - but the visitors, top of League Two, ran out 3-1 winners against nine men, as the home side had Sam Togwell and Andy Yiadom sent off.
Sam Winnall struck his first senior hat-trick as League One Barnsley beat League Two promotion hopefuls Burton Albion 5-0, with Devante Cole - son of former Manchester United and England striker Andy - also scoring.
Tom Bradbrook scored the winner for Conference side Dartford - after elder brother and team-mate Elliot had also struck - in a 4-3 victory at Kent neighbours Bromley, of the Conference South.
It was the day's joint-highest scoring match, as MK Dons matched it with a 4-3 win at League One rivals Port Vale.