Englishmen David Lynn and John Bickerton share second at 13-under and Craig Hainline, Stephen Dodd, Des Smyth and overnight leader and defending champion Niclas Fasth are three off the pace at minus 12.
Florioli, who began the third round four shots behind Fasth, opened with two pars before he carded his first birdie of the day at the par-5 3rd, a hole he eagled on Friday.
The Italian parred the fourth but then ran home five birdies in a row, starting at the fifth, for a front-nine 30, his lowest nine-hole score on the European Tour.
Florioli carded another birdie at No. 11, but failed to pick up another birdie on the back, despite the fact that he hit every green in regulation on the second nine.
'I had a lot of chances on the back nine but I left the putts short,' said Florioli. 'I played very well on the second nine but kept having downhill putts. I played well and put the ball close to the hole.'
Florioli has finished second twice on the European Tour and held the lead of the 1998 English Open through 16 holes only to drop the title to Darren Clarke.
'I have a chance tomorrow, so I will try my best.'
Lynn fired an 8-under 64 on Saturday, thanks to six birdies
'I'd love to go out and play the same as I did today,' said Lynn, whose 64 was his lowest on the European Tour. 'I don't think I missed a shot out there tee to green.'
Bickerton missed a two-foot par save at the second but rebounded with two birdies in his final three holes to shoot 69.
'I played all right, but missed a short putt early on at the second hole for par,' said Bickerton, who was alone in second after Friday's second round. 'Then I got a little edgy and wasn't getting the ball up to the hole. They are alright for pars but when you have a 10-foot birdie and keep lagging it to the hole, it is not much fun.'
Fasth started 4-over through his first four holes but came back to post an even-par 72.
Andrew Oldcorn is alone in eighth at 11-under while Fredrik Henge, Massimo Scarpa, Markus Brier and Jose Manuel Lara round out the top-10 at minus nine.
Click here for full-field scores from the Madeira Island Open