Jonas gave the visitors the lead on five minutes but Radamel Falcao levelled the score a minute later.
Valencia were superior in the first half but Diego Simeone's side improved in the second period and thought they should have been awarded a penalty for a handball by Jonas.
Ernesto Valverde's side are still fighting to qualify for the Champions League next season and began the game brightly, showing more ambition in the opening 45 minutes than any other team to have visited the Calderon all season.
They had their first attempt on goal after just two minutes, Pablo Piatti dispossessing Diego Godin down the right-hand side but his powerful cross found no-one and skidded past the far post.
However, it did not take long for the visitors to take the lead. Full-back Joao Pereira's cross went through the Atletico defence and the ball fell to Jonas, who controlled and then shot through Thibaut Courtois' legs and into the net.
Atletico had offered little in the opening exchanges but responded immediately with an equaliser. Arda Turan turned his marker on the left-hand side to deliver a cross into the box and Falcao timed his run perfectly to meet the cross alone and volley into the net and record his 23rd goal in the league this season.
The goal was Atletico's only proper chance in a first half in which they were outplayed by their opponents, and were grateful, not for the first time this season, to their goalkeeper Courtois.
The Belgian tipped a venomous shot from Dani Parejo over the bar with his fingertips and then made a superb double save, first from Piatti and then from Jonas, to keep the score level at the break.
Atletico were a much-improved side in the second half, allowing Valencia far less space while also creating chances for themselves in five minutes of sustained pressure on the visitors' goal.
Valencia goalkeeper Diego Alves had to be quick off his line to beat Diego Costa to a through ball by Falcao, and the Brazilian then kept out a header form Godin.
Atletico's players strongly appealed for a penalty from the resulting corner, when Jonas appeared to block a shot by Falcao with his hand, but the referee kept his whistle in his hands.
Valencia rode the pressure out and there were few chances in the remaining half an hour, the best of which was a long-range effort from Parejo which sailed wide of Courtois' goal.
The result was not of much benefit to either side. Atletico remain in third place, failing to capitalise on Real Madrid's 1-1 draw with Real Zaragoza on Saturday, while Valencia surrendered fifth position to Malaga and dropped down to sixth and out of the Champions League spots.