Alvaro Morata and Claudio Marchisio had put the Serie A leaders ahead at the break but the home side deservedly earned a point
The reigning champions looked set to take all three points when Vidal stepped up to take an 82nd-minute spot-kick, but the Chile star missed the target, leaving Juve to rue not capitalising on Roma's 0-0 draw earlier in the day.
Cesena's battling display gave little indication of their precarious position in the relegation zone, with Milan Djuric giving the hosts a deserved lead 17 minutes in.
Juve, shocked into action, were level just before the half-hour mark, Alvaro Morata finding the net.
Claudio Marchisio then put the visitors ahead six minutes later, but Cesena rallied after the break and enjoyed significant periods of control before Brienza struck the leveller with 20 minutes left.
Vidal's failure to net from the spot late on, though, summed up an opportunity missed for Massimiliano Allegri's side.
Juve showed few signs of their imperious form during the early exchanges, relying on goalkeeper Gianluigi Buffon to keep them on level terms.
The Italy shot-stopper first palmed Gregoire Defrel's effort around the post, before then denying the Frenchman again in the 10th minute after he had seized on an error by Leonardo Bonucci.
Cesena's bright start eventually paid off in the 17th minute and Defrel was at the centre of things again, this time robbing Andrea Pirlo of possession before playing a pass into Djuric in the area, with the Bosnian firing a shot under Buffon.
That goal seemed to jolt Juve into life and Allegri's side were level 10 minutes later, Morata heading in Paul Pogba's excellent left-wing cross.
Uncertainty in the Cesena defence then allowed Juve to complete the turnaround in the 33rd minute.
Stefano Lucchini and Giuseppe De Feudis failed to deal with Morata's flick-on from a Patrice Evra throw-in and Marchisio was on hand to prod the ball beyond Nicola Leali.
Pirlo almost opened up a two-goal lead for Juve just before the break, but his powerful 25-yard drive flew just wide of the left-hand post.
Cesena began to cause problems again early in the second half, with Defrel's low drive across the face of goal in the 54th minute giving Buffon something to worry about.
Juve continued to invite pressure and the home side went close again with 64 minutes on the clock, Brienza this time lashing a half-volley just over from just inside the area.
Brienza was not so wasteful a few moments later, though, as the attacker pounced on Djuric's lay-off and drilled a low shot beyond Buffon.
Cesena's efforts looked as though they would count for nothing when Lucchini handled the ball in the area with eight minutes left.
But Vidal sent the resulting spot-kick wide of the left-hand post and Cesena ultimately held on to secure a deserved draw.