Harris hit 78 off 32 balls, including eight fours and five sixes and claimed 3-33 off seven overs while Laing hit a quickfire 80 off 47 balls (12 fours and three sixes) and claimed 2-25 off eight overs.
Scores were Couples 173-9 off 36 overs, Shaw Park 177-3 off 15.2 overs.
Couples openers Barrington Christie 33 (four fours and two sixes) off 27 balls and Lenroy Henry, 20 runs, posted 49 before Christie was trapped leg before by Calvin Aaron.
Couples slipped to 76-4, before Warren Medwynter (21) joined skipper Wentworth Pendley (37) in a vital fifth wicket stand of 60 before spinners Harris and Laing wove a web around the remaining batsmen. Only last man in, Evan Gordon with 20 not out, offered resistance.
Couples struck early when the hard hitting Howard Harris was caught on the boundary off the first ball he received from Nedroy Pinnock with the score on five.
Shaw Park then ran amok with Harris and Laing tearing into the bowling. The score raced to 148 in the 12th over when Laing was caught off the bowling of Collin Jackson.
Harris went 22 runs later, but Norris Campbell saw Shaw Park through to their eighth victory in the preliminary round.