The chairman, millionaire Stephen Lansdown, thought Taylor would be the man to rescue the Robins' sagging play-off hopes.
And during this game it was not difficult to see why the ex-Watford manager did not fancy a job at Ashton Gate as City struggled to raise the tempo of a lacklustre match.
Tinnion has given up playing after 500 games for City to concentrate on his job as manager and gambled here by fielding three teenagers who had made just nine starts between them.
The inexperience showed but as the three - Dave Cotterill, Scott Brown and Scott Golbourne - settled in City had an astonishing piece of good luck.
Their goalkeeper Steve Phillips sent a clearance straight to Simon Johnson, a 22-year-old on loan to Barnsley from Leeds. Johnson made space well for a clear shot but then dragged it wide of the target.
Barnsley, who have had their own managerial problems with the departure of Paul Hart, were to regret that miss.
It was Cotterill, starting his fourth league game, who lifted City with a searching cross from the right flank midway through the first half and then Brown hit the bar from 22 yards.
There was a second near miss for City when Steve Brooker headed against the underside of the bar from a rare corner, but then on the hour City again found fortune smiling on them.
Barnsley's Michael Chopra, who had been booked for a run of the mill foul in the first half, saw yellow again followed by red when he went down under a centre circle challenge from Tom Doherty.
Referee Mike Fletcher accused Chopra of diving.
Doherty himself went into the book eight minutes later after a touchline fracas with Chris Shuker.
Shuker, who had been booked earlier, escaped further punishment although the free-kick was given to City.