Joe Cardle's first-half goal put the Pars in the driving seat but Nick Ross grabbed a deserved leveller after 75 minutes.
With Hibernian not in action until Sunday, victory would have lifted Jim McIntyre's struggling side above their relegation rivals.
But their wretched home form continued, with Dunfermline now having failed to win in 14 league matches at East End Park this season.
Pars manager McIntyre made three changes to the side that lost 4-1 to Rangers last weekend.
Cardle, Martin Hardie and Kyle Hutton came in to the side, with Paul Burns, Mark Kerr and Liam Buchanan dropping out.
Inverness manager Terry Butcher was without the suspended Steve Williams. The Englishman was sent off against Celtic last weekend and David Proctor replaced him in central defence.
There was a huge incentive for Jim McIntyre's side but their home record suggested this fixture would not be easy.
Inverness were looking to pull further away from Hibs and Dunfermline, and Richie Foran had an early effort that was blocked.
Caley were more dangerous in the opening stages and Greg Tansey's low drive flashed wide after 12 minutes.
The visitors were trying to play off giant French striker Claude Gnapka and his lay-off found Ross, but Chris Smith saved comfortably.
Gnakpa's awkward, bustling style unsettled Dunfermline and he fired a rising drive over the crossbar in 25 minutes.
The Pars offered little going forward but winger Cardle burst to life with a mazy run before his shot was blocked.
Caley had more creativity and again cut through Dunfermline on 32 minutes, but Shane Sutherland blazed over.
Pars full-back Jordan McMillan then had to clear off his line as Sutherland tried to connect with Jonny Hayes' cross.
Irish winger Hayes grew into the game and drilled a shot wide minutes before half-time.
But Dunfermline then stunned Inverness by taking the lead in 45 minutes.
Cardle won a free-kick on the edge of the box and Martin Hardie's effort crashed off the bar. Caley couldn't clear the loose ball and Cardle reacted quickest to drill home from six yards.
Dunfermline had a chance to make it 2-0 minutes after the break but Paddy Boyle did not connect properly with Hayes' cross.
Inverness responded well to that let-off and McMillan's last-ditch tackle foiled Ross after a swift break.
The Pars tried to get Cardle on the ball as much as possible and Proctor scrambled clear after a dangerous cross from the winger in 55 minutes.
Proctor was not so reliable moments later when he missed a through ball and gifted Andy Kirk a free run on goal.
The Northern Irishman could have squared to team-mates but went for goal and Ryan Esson touched the shot wide.
Sutherland headed over from eight yards in 65 minutes as Caley chased the equaliser.
But Dunfermline were full of confidence and Gary Mason's 20-yard drive rolled inches wide.
Inverness kept going and the equaliser finally arrived in 75 minutes. Hayes was the provider with a low cross and Ross swept in at the back post.
Neither side gave much away in the closing stages but Esson produced a brave save at Liam Buchanan's feet.
The Dunfermline striker then headed over from just six yards as his side's search for a home win continued.