The 43-year-old Campbell, ranked 607th in the world having been as high as 13th at the start of 2006, fired a two-under-par 69 in testing conditions to record a five-under total of 137 that left him five strokes behind English leader Fisher (67).
Campbell, who tied for 47th place at last week's Dunhill Links Championship in Scotland, could barely contain his delight after climbing into contention on the Algarve.
"It's actually been quite a tough couple of days in the wind but it's nice to finally put a few good scores together," the 2005 US Open champion said.
"One thing I've been working on mentally is to just enjoy the game. It's only a game of golf so just go out there and if you play well it's a bonus and if not it's no big deal."
Campbell last registered a win in the 2005 World Match Play Championship at Wentworth and has endured some torrid seasons including 2010 when he made just one cut and earned less than 14,000 euros on the European Tour.
"I'm feeling pretty confident right now which hasn't happened for a while so I'm really looking forward to the weekend. It's been a long time since I've been in contention," said the Kiwi who has had a home in England for several years.
Triple major-winning Irishman Padraig Harrington is also doing well in Portugal and he matched Fisher's 67 to finish four off the lead on 136.
"It was all going nicely ... but I'm a bit upset about making two three-putts at the end," said Harrington who has not won a regular tour event since the 2008 US PGA Championship.
In joint second place on 135 were Austrian Bernd Wiesberger (65) and Scot Stephen Gallacher (70).
- Dunhill Links Championship