Wesley's backs came to the fore, linking well and a skip pass put Heap over to the right of the posts. Out-half David Smith's conversion attempt bounced back off an upright.
Connemara, who have now lost their last four games, bounced back with two penalty goals from the boot of David Newman.
But Wesley centre Alan Thompson swooped to intercept a pass in midfield and beat the cover for an unconverted 30th-minute try.
The hosts, leading 10-6 at the break, should have made the visiting All Blacks pay for some slack defending early in the second half when full-back Alan Large was twice put into space but the attacks broke down.
Newman cracked over his third penalty to close the gap and the Galway men missed out on a glorious chance to grab a try when, with an overlap on, the final pass went astray.
However, a second Smith penalty was enough to see Wesley claim their tenth win of the campaign.
Wesley are ten points behind pace-setters Ballynahinch who managed to get back to winning ways with a thumping 46-7 victory over City of Derry at Ballymacarn Park.
'Hinch grabbed their 18th win in 31 league clashes against Ulster opposition with Stuart Morrow and David Harris scoring two tries apiece. Chris Napier, Stuart Megaw and Adam Bartholomew also bagged tries for the County Down side.
Under-20 player Dave Murphy touched down for the second successive game as Corinthians won 14-9 at Waterpark to score their third win in five league games.
Nenagh Ormond continued their excellent league form at home to Ulster clubs - they completely dominated Portadown for a 57-7 success on Saturday for what was their fifth win in eight league clashes at home to clubs from the north.
Nenagh ran in eight tries with Richard Dodd (2), Damien Gavin, Ger Hermse, Trevor Connolly, John Keehan, Michael Fogarty and Trevor Powell all off the mark. Noel O'Meara's Tipp side are now right in contention having moved from sixth to fourth in the table.
Gareth Martin took his try tally for the league season to nine as Banbridge edged Ards 27-20 in an all-Ulster duel at Hamilton Park. Teenage winger Jordan Millar scored one of Ards' three tries to take his tally to 12.
Second-placed Wanderers, who have a game in hand on 'Hinch, got the better of Queen's University at Dub Lane, winning 28-3 with flanker Emmet Wardell and centres Ronan Likely and Jimmy Ferris sharing out their tries.
Wanderers have scored 14 tries in their last three games - all against Ulster opposition - and have quickly become the division's form team.
At Hatrick Park, Instonians lost ground on the top two as Rainey Old Boys pipped them 19-18. Eleven points from the boot of Michael Glancy, allied to a Darryl Porter try and a drop goal from Jerome McMurray, were key for Rainey as they handed 'Inst their third straight league loss.
DIVISION THREE: RESULTS -
Ards 20 Banbridge 27, Hamilton Park
Ballynahinch 46 City of Derry 7, Ballymacarn Park
Nenagh Ormond 57 Portadown 7, New Ormond Park
Old Wesley 13 Connemara 9, Donnybrook
Queen's University 9 Wanderers 28, Dub Lane
Rainey Old Boys 19 Instonians 18, Hatrick Park
Waterpark 9 Corinthians 14, Ballinakill
Sunday's Well v Bruff, Musgrave Park (Postponed)