Facing a side that started the evening second in League Two, Morecambe produced an excellent display to clinch a vital fifth home win of the campaign.
The first half was an end-to-end affair with Brentford forging a great opening in the first minute when Charlie MacDonald's cross evaded Dave Artell and found Jordan Rhodes but the striker's shot was tipped away by Barry Roche.
At the other end the Shrimps' top scorer Howe forced Ben Hamer to make a decent save from a near post header and then poked a shot wide with only Hamer to beat after latching on to Craig Stanley's pass.
At the other end Roche maintained his fine recent form with a stunning diving save to deny Rhodes with another shot on the turn, this time after he'd been found by Sam Wood.
But the game was too open to remain goalless for too long and it was the Shrimps who gained the upper-hand after 23 minutes when Fraser McLachlan's long ball beat the Brentford defence and Twiss was free to lash home his first goal of the season.
The second half saw few chances as Morecambe defender stoutly. MacDonald looked set to have a half-chance before a superb Danny Adams tackle on 53 minutes but that proved to be the final moment of threat for the Shrimps.
As Brentford pushed bodies forward in the hunt for an equaliser, McIlroy's side struck for a second time.
Man of the match Neil Wainwright burst down the left and ran into the area before squeezing the ball across the six-yard box for Howe to score from close range.