Third-placed 'Quins, who initially were 7-0 down after Tom Allen's fine second-minute try for the visitors, exploded into life in the final ten minutes of the first half.
Racing to their first home win over the Connacht men since 2000, Bester's men ran in late scores from Strauss, Stuart Lambe, Paul McKenzie - scoring his fourth of the campaign - and Mark Kettyle, adding to an earlier Ian Humphreys effort, for a 35-10 half-time buffer.
More of the same followed on the restart with Lambe, Stuart Wilson, Strauss and flanker Colin Atkinson on target before Strauss rounded off his superb 33-point performance with a third in the closing stages.
Elsewhere, Cork Constitution ended their barren run of three defeats in four games with a comprehensive 54-22 thumping of a hapless County Carlow.
Winger Cronan Healy pocketed three of their seven tries, aided by the 19-point boot of scrum-half Pat McCarthy.
Although Carlow's Richie Murphy lost the kicking duel - notching 17 points - he offered the midlanders' best attacking threat after winger Ross Jackson's intercept try on the half-hour.
Buccaneers had both Chris Keane and Niall Smullen sin-binned in the second half of their 30-10 loss to Clontarf at Castle Avenue. The Pirates started well with Eamon Molloy grabbing an early converted try, but 'Tarf - who sit joint-top with Shannon now on 28 points - blazed back for a 20-7 break advantage.
Tries from Dave Moore, Warren O'Kelly, Dave Hewitt and a last minute one from prop Niall Carson saw Phil Werahiko to their fourth bonus point. Returning centre Shane Moore brilliantly set-up fullback Hewitt for 'Tarf's third touch down before half-time, and their 350th try in AIL history, making the north Dubliners the ninth club to hit such a mark.
Champions Shannon picked up their sixth win at Thomond Park, but they were made to work for a 25-18 verdict by Dublin University.
Hooker Nigel Conroy and centre Brian Tuohy (2) struck for Shannon's three tries - all in the first half - as they led 25-7 at the interval.
Ireland Under-21 Jamie Heaslip had earlier breached the home side's line, and although Trinity scrum-half Matt D'Arcy also muscled over in the second half - allied to two penalties from the boot of Keelan McGowan - Shannon held on.
Down the road at Dooradoyle, two penalties apiece from Alan Purcell and Gerry Hurley were enough for Garryowen to pick up their third consecutive win - 12-8 against bottom side Lansdowne.
Ulster back Paddy Wallace, meanwhile, had a happy return to his old college when scoring three penalties and a drop goal in Ballymena's 17-9 defeat of an off-form UCD.
The fifth-placed students, losing for only the second time this season, were 6-3 up at the interval after Eoghan Hickey - who started the afternoon on 98 points - hit a penalty and snap drop goal to become the first top flight player to break the 100-point barrier for the campaign.
The Braidmen's quick repost on the restart saw Henry Head set up second phase ball for Ulster wing Andy Maxwell to nip in out wide.
Wallace added a penalty, sandwiched by a monster Hickey effort, and two more kicks on 62 and 85 minutes to end a two-game losing streak for Steph Nel's side.
Blackrock College are still without a win in Tyrone since 1993, after recently-appointed Ireland Under-21 captain Gareth Steenson drove Dungannon to a 17-10 success.
Indian winger Ajay Subherwal did the donkey-work for Andy Hughes to notch 'Gannon's first try after only ninety seconds.
Steenson converted and added a twelfth minute penalty before Conor Kilroy replied with one of his own in injury time.
Despite conceding a 50th-minute try to home skipper Paul Magee, 'Rock fought back with centre Andy O'Neill bagging his fifth of the season ten minutes from time, but it proved not enough.
In Division Two, Dolphin lost their grip on top spot despite Ireland Sevens star Tomas O'Leary scoring his eighth try of the season, in a 13-13 draw with Terenure College.
UCC now lead the way - showing the strength of College rugby in the country - on points difference, and on the footing of their seventh win from ten. Number eight Rory Geogeghan put in a man-of-the-match display as he scored a try, along with Denis Hurley, Richie Lane and prop Tim Ryan in their 35-19 defeat of Old Crescent.
Greystones meanwhile, continue to devour up all that Division Three can throw at them. They ran in eleven tries when posting their tenth win of the campaign at Dr. Hickey Park on Saturday.
Fullback Dave McKechnie (2), centre Conor McNaughton (2), flanker Rob Connolly (2), second rows Darren McGettigan and Graham Murphy, wing pairing Ronan Carroll and Stuart O'Connell and hooker Ronan Willis were all on target with number 10 Warren Edwards converting nine and adding a penalty.
'Stones chasers Clonakilty scored a 43-13 win at Old Wesley with Derek Dillon and David Lombard bagging a brace each.
Connemara flanker Noel Walsh scored two in their five-try 34-0 trouncing of strugglers Ballina, while former Belfast Harlequin Ajay Derwin grabbed a 19-point haul as mid-table Ards claimed their fourth straight win - beating Corinthians 34-26 at Hamilton Park.
Belfast Harlequins 68 Galwegians 10, Deramore ParkClontarf 30 Buccaneers 10, Castle AvenueCork Constitution 54 County Carlow 22, Temple HillDungannon 17 Blackrock College 10, Stevenson ParkGarryowen 12 Lansdowne 10, DooradoyleShannon 25 Dublin University 18, Thomond ParkUCD 9 Ballymena 17, Belfield
Barnhall 19 Midleton 18, ParsonstownMalone 21 De La Salle Palmerston 20, Gibson ParkSt Mary's College 15 Old Belvedere 9, Templeville RoadTerenure College 13 Dolphin 13, Lakelands ParkThomond 20 Bective Rangers 18, Fitzgerald ParkUCC 35 Old Crescent 19, The MardykeUL Bohemian 42 Young Munster 31, Thomond ParkWaterpark 15 Ballynahinch 19, Ballinakill
Ards 34 Corinthians 26, Hamilton ParkConnemara 34 Ballina 0, Monastery FieldGreystones 76 Banbridge 30, Dr Hickey ParkOld Wesley 13 Clonakilty 43, DonnybrookQueen's University 25 Portadown 15, Dub LaneSkerries 22 City of Derry 18, HolmpatrickSunday's Well 15 Bruff 17, Musgrave ParkSuttonians 23 Instonians 21, JJ MacDowell Park