It was all Malone in the opening quarter as Josh Pentland landed an early penalty and strong-running centre Stuart Wilson burst through for a breakaway try which out-half Pentland converted.
The Ulster underage player knocked over penalties after 21 and 27 minutes, boosting his personal haul to 11 points, as the Belfast outfit, who are preparing for the start of AIB League Division 2 next week, took a tight grip on proceedings.
But the 'Well launched a fiery fightback in the second half. The Division 3 side, coached this term by Keith 'Cheeky' Murphy, grabbed a deserved try through new scrum half Ruairi Geary.
The 'Well, who were without a number of key players, got right back into contention with half-backs Tom Parker and Geary directing matters behind a very competitive pack.
After a John Verling penalty got the hosts on the scoreboard, the Corkmen followed up with Geary's try, scored off a big drive from close range.
Verling added the conversion and though further pressure came on the Malone defence from Barry Hanrahan and Chris Long, the visitors maintain their lead of six points to secure a second round date at home to Blackrock College on October 17.
Coached by Andy Ward and Adam Larkin, Belfast Harlequins will face a trip to UL Bohemians in the next round after coming through their first round encounter with Naas at Deramore Park.
'Quins overcame an early Naas onslaught to run out 32-10 winners in an entertaining tie. It was the half-time introduction of new signing John Mills which put this game beyond any doubt, with the New Zealander involved in all of the hosts' second half scores.
Mills, who only arrived at the club on Thursday, made quite an impression at out-half.
Naas began brightly and a third minute penalty from David Aherne sent them into the lead.
Although 'Quins levelled through a Rory Blake-Knox drop goal, the Kildare men continued to look dangerous. Johnny Holmes finished well when scoring the visitors' only try after 30 minutes.
Aherne's conversion briefly squared it up at 10-all, but first half tries from Colin Atkinson, David Creighton and Samoan prop Alatise Ale handed 'Quins a 22-10 interval lead.
Naas failed to score in the second half as they came under strong pressure from the current Ulster Senior League leaders.
Harlequins strengthened their pack with the additions of Mark McGrath and Andrew Joseph inside 15 minutes of the restart, and with fellow replacement Mills firing on all cylinders, they plotted a course for round 2.
Meanwhile, AIB League Division 2 newboys Corinthians needed extra-time to see off Wanderers by 33-20 at Corinthian Park.
A converted try from new Connacht winger Thomas Timani, a recent arrival from New Zealand, a penalty from Wayne Williams and a drop goal from Darin Claasen saw Corinthians come out on top in extra-time.
Shane Moynihan, the Galway side's new out-half, scored an early try and Pat Cunningham showed great strength to break a tackle for try number 2.
But Wanderers closed the gap back to 14-8 with a terrific try from former underage international Paddy Brophy.
Further tries from Craig Dalton and former Connacht Under-20 flanker Philip Rowe edged the Dubliners ahead, before a Moynihan penalty sent the game into extra-time at 20-all.
Corinthians will be away to UCC in the second round, while Barnhall, 22-3 conquerors of Suttonians, will also be on their travels to Cork to face Dolphin.
The Blue Bulls had tries from Jerome Bidau and impressive flanker Lorris Zaglio, as well as a healthy kicking contribution from Leo Quinn, as they got the better of Suttonians at Parsonstown.
Elsewhere, Navan, the 2008 AIB Junior Cup champions, made a winning senior bow as they secured a 20-10 home victory over Instonians, while Bruff, Queen's University, Greystones, Thomond, UCD and Old Crescent all claimed away wins - Queen's 43-3 defeat of County Carlow catching the eye the most.
Paul Karayiannis, David McIlwaine, Mark Robinson (2), Gareth Megaw, Andy Linton and Chris Quinn crossed the Carlow whitewash as a rampant Queen's tallied up seven tries at Oak Park.
McIlwaine kicked four conversions to complete the Belfast students' scoring, while Richie Whyte kicked a penalty for Carlow's only points.
Greystones prevailed against DLSP at Kilternan, with tries from winger Tom Parker, scrum half Frank Jones and prop Bobby Clancy guiding the Wicklow men to a 17-11 win.
The big Donnybrook derby went the way of Bective Rangers on a 21-20 scoreline and Terenure College, under the tutelage of new director of rugby Ian 'Moggy' Morgan, showed some good early season form by hammering Connemara 59-17 at Lakelands.
AIB CUP FIRST ROUND: Saturday, September 26
Sunday's Well 10 Malone 16, Musgrave Park
Barnhall 22 Suttonians 3, Parsonstown
Belfast Harlequins 32 Naas 10, Deramore Park
Clonakilty 16 Bruff 26, Shannonvale Cross
County Carlow 3 Queen's University 43, Oak Park
Corinthians 33 Wanderers 20, Corinthian Park (after extra-time)
De La Salle Palmerston 11 Greystones 17, Kilternan
Dublin University 29 Banbridge 14, College Park
Highfield 15 Thomond 17, Woodleigh Park
Lansdowne 28 Ards 19, The RDS
Midleton 16 UCD 19, Towns Park
Navan 20 Instonians 10, Balreask Old
Nenagh Ormond 24 Portadown 5, New Ormond Park
Rainey Old Boys 17 Old Crescent 27, Hatrick Park
Terenure College 59 Connemara 17, Lakelands Park
Bective Rangers 21 Old Wesley 20, Donnybrook
SECOND ROUND FIXTURES (ties to be played on October 17):
Match 1: St. Mary's College v Bruff
Match 2: Young Munster v Terenure College
Match 3: UL Bohemians v Belfast Harlequins
Match 4: Dungannon v Queen's University
Match 5: Navan v Garryowen
Match 6: Bective Rangers v Ballymena
Match 7: Ballynahinch v Cork Constitution
Match 8: Lansdowne v Nenagh Ormond
Match 9: Thomond v UCD
Match 10: Malone v Blackrock College
Match 11: Old Crescent v Clontarf
Match 12: UCC v Corinthians
Match 13: Old Belvedere v Greystones
Match 14: Galwegians v Dublin University
Match 15: Shannon v Buccaneers
Match 16: Dolphin v Barnhall
The winners from round two will be entered into further open draws for round three, the quarter-finals and semi-finals.
The final will be played on January 30, 2010. The draw for the AIB Junior Cup will be made at a later date.