For 1986 Cogan joined Patrick Racing to drive the No. 7 7-Eleven March 86C-Cosworth DFX. At the season opening Dana 200 for Special Olympics at Phoenix International Raceway Cogan scored his first Indycar win, leading 2nd place Tom Sneva by a lap. It was also the first time Cogan led the CART standings in his career. With 13 laps to go in the Indianapolis 500, Cogan made a bold move to pass Rick Mears and Bobby Rahal in less than a lap when both were held up by the slower car of Randy Lanier. Despite his car conspicuously oversteering in the turns, Cogan pulled away to a 3-second lead before a caution came out on lap 195 for a crash by Arie Luyendyk in turn four. Cogan did not get a good restart on lap 198 and was passed by Rahal, eventually finishing in 2nd place. Cogan still led the standings after Indianapolis but suffered retirements in seven of the fourteen remaining races and fell to 6th in the championship.