Hawks were on course for a landslide at Old Anniesland as they opened up a 25-0 lead at the break, however they lost their composure and were unable to add to their try tally.
Their counters came from Murray Strang, Greg Francis and Nick Cox, while Mike Adamson slotted two conversions and a penalty treble.
Hooker Dougie McLaren claimed High's consolation effort, but they took great credit for their defensive display after the break.
Ross Cook was the man who mattered for Muir as he snatched the late try which inflicted a shock 22-20 defeat on BT Premiership dark horses Ayr at Millbrae.
The hosts had looked destined to hold out for their fourth triumph on the trot - until the full-back had the final say.
The seasiders broke the deadlock with a Nick Lavelle penalty in the sixth minute but Muir seized the initiative with an opportunist score by Angus Martyn, goaled by Cook
The rattled home troops replied in positive fashion to create a superb touchdown for flanker Paul Burke and stretched their advantage in the approach to the interval thanks to the power and pace of substitute Colin White.
He made the break that led to scrum-half Ally MacFarlane nipping over with ease, before Lavelle bagged the extra points.
The restart signalled a Muir rally with Cook slotting a penalty, but they were on the back-foot again as Tippett ploughed over.
The end-to-end action continued when winger Rory Couper went over for the visitors, Cook converting to set up a tense finale.
And Cook was back in the spotlight when it mattered, latching on to a Couper pass to grab the decider.
Watsonians inflicted another dose of misery on BT Premiership basement boys Grammar, romping to an easy 52-17 success at Myreside.
Scotland prospect Andy Skeen led the Sonians charge with two touchdowns, the others being snapped up by Ally Rowe, Danny Moussa, Robin Holroyd and Matt Couper.
Mike Ker kicked four conversions and four penalties to complete the rout.
The outclassed Dons could only respond with tries by Matt Quilty and Rob Currie, both goaled by Rod Seib, who also had a penalty.
Hawick's mini-revival came to an abrupt halt at Goldenacre as they plunged to a 29-0 BT Premiership defeat at the hands of a clinical Heriot's outfit.
The Edinburgh side had too much pace and power in their backline and the only surprise was that they did not pile up more points.
Their tries came from Steve Manning, Neil Robert, Marc Teague and Cammy Goodall, with James Thomson and Graham Wilson sharing the boot points.
Only 10 points separated the sides at the end of the regulation period - then came the avalanche which
buried the Borderers and made sure of the crucial bonus award.
The Currie scorers were playmaker Ally Warnock, Andy McMahon (2), Chris Browne and Ross Weston with a 60-metre dash.
At Dumbreck, Edinburgh Accies took the spoils with a 22-14 win, having led 17-7 at the break. Mike Campbell, David Ratteray and Joe Edwards had tries for Accies, while John McCrossan and Ross Gillies notched scores for Cartha with Ruraidh Jackson landing both conversions.
That win takes them to top of the table as GHA slip back, despite recovering to 21-19 after being 21-0 down at Riverside. The reward for their fightback is a bonus point. Clark Laidlaw and Ross Goodfellow had first half tries, Paul Pringle added one just after the break and Gary McGarva slotted all three conversions, but GHA hit back with tries from Jon Welsh, Iain Kennedy and Rory Watson, the last from inside his own twenty two. James Noonan had two conversions out of three as GHA slip to fifth in the table with Jed moving to third behind Stirling County, who beat Hillhead-Jordanhill at Bridgehaugh by 45-3.
Haddington stay top of Premier 3 after a 39-13 win over Murrayfield Wanderers. Donald Snodgrass grabbed a try double, while Rhodri Thomas, Andy Douglas, Jamie Cooper and Ian Henderson all claimed one apiece. Cooper added three conversions and a penalty with Ken Boyd also knocking over a conversion.
Musselburgh leapfrog Ellon into second spot in the Premier 3 table after the two clashed at Stonyhill, with the home side taking the points thanks to a 37-19 win. Cammy Walker, Graham Wells, Ross Connerton, Scott Porteous, Barry Morrison and Greig Walker spread the tries around for Musselburgh with Angus Stewart landing two conversions and a penalty.
Dunfermline move into third place after winning 30-21 against Livingston at Almond Park, while West keep up their challenge after coming away from the Gytes with a 20-17 win over Peebles - tries coming from Bulloch, Wright and Park. Kirkcaldy, meanwhile, had to come from 0-3 down to win 81-3 against Cambuslang at Beveridge Park.