1961 Dallas Cowboys season The 1961 Dallas Cowboys season was their second in the National Football League . The team finished with 4 wins , 9 losses , and 1 tie , placing them 6th in the Eastern Conference . Offseason . The Cowboys participated in their first NFL college draft following the 1960 season . Despite owning the league ' s worst record , the team picked second overall because the expansion Minnesota Vikings received the first overall selection . However , the team previously traded away their first round pick in the 1961 draft to the Washington Redskins for quarterback Eddie LeBaron . The Cowboys had another selection in the first round ( 13th overall ) that they acquired from the Cleveland Browns , and with that selection they chose defensive lineman Bob Lilly from Texas Christian University . Other notable selections in the draft included offensive linemen E . J . Holub , Billy Shaw , and Stew Barber . However , all three chose to sign with teams in the rival American Football League . Other notable acquisitions by the Cowboys during the offseason included trading for linebacker Chuck Howley from the Chicago Bears , and signing rookie free agents Amos Marsh and Warren Livingston . Schedule . Season recap . Coming off of a winless first season , the Cowboys wasted no time getting their first win in franchise history in their second season , a 27 – 24 home victory over the Pittsburgh Steelers in the season opener , the winning points coming on a last second field goal . The Cowboys would go on to win two of their next three , both easy victories coming over the expansion Minnesota Vikings , and a month into the season the Cowboys found themselves tied for first in the Eastern Conference with a record of 3 – 1 . While much improved over their first season , the Cowboys would continue to be outclassed by the better teams in the league . In between their victories over the Vikings the Cowboys suffered a 25 – 7 defeat at the hands of perennial powerhouse Cleveland . The following weeks after their 3 – 1 start quickly dampened any realistic chance they had of contending for the Eastern Conference championship , with home losses to the New York Giants and the defending champion Philadelphia Eagles coming by a combined score of 74 – 17 . However , the following week the team stunned the Giants at Yankee Stadium , 16 – 14 , on another late field goal , and the Cowboys found themselves with a winning record at the midway point of the season at 4 – 3 . Unfortunately , it was all downhill from there , as the Cowboys didn ' t win another game all season . The Cowboys gave up 28 points or more in each of their remaining seven games , and were beaten by 14 or more points in five of them . The Cowboys managed a tie against the woeful Washington Redskins in week 10 , a game in which quarterback Don Meredith , who had been splitting playing time at the position with Eddie LeBaron , suffered an injury to his throwing shoulder , and wouldn ' t play again the rest of the season . The final game of the season saw the Cowboys lose to the Redskins at D . C . Stadium ( the Redskins first win at their new home ) , 34 – 24 , the only win of the Redskins season . Offensively , the Cowboys were an improved lot across the board . The offense moved the ball at a decent pace , finishing 8th in the league in yards gained . Quarterbacks Eddie LeBaron and Don Meredith had quality targets at the receiver position , which helped the team finish 6th in passing yardage . Veteran Billy Howton established a career high in receptions with 56 , and Frank Clarke developed into one of the league ' s top deep threats , averaging 22 . 4 yards per catch and scoring 9 touchdowns . Tight end Dick Bielski represented the Cowboys at the Pro Bowl . The Cowboys may have showed the most improvement in the running game . Rookie Don Perkins was one of the leagues top running backs with 815 yards , and Amos Marsh and J . W . Lockett contributed as well , improving the Cowboys to 10th in total yards rushing , and improving the yards per carry from 3 . 4 in 1960 to 4 . 4 in 1961 . On the negative side , the offense turned the ball over 48 times during the season , second worst in the league , and the offensive line continued to struggle protecting the quarterback . The team only scored 236 points ( 13th in the league ) despite the Cowboys improved offensive play . Defensively , the team continued to struggle against the run , allowing 2161 rushing yards ( 12th in the league ) and 4 . 8 yards per carry . Against the pass , the secondary allowed too many long completions ( a league worst 15 . 7 yards per completion ) and the defensive front didn ' t apply much pressure on the quarterback . The defense did make more than its share of big plays , forcing 43 turnovers . Cornerback Don Bishop had 8 of the defense ' s 25 interceptions . Rookie kicker Allen Green struggled much of the season . His 36 . 7 yards per punt was worst in the league , and after going 5 of 15 on field goal attempts ( though two of the field goals provided the game winning points ) he was replaced by Dick Bielski , who made 6 out 9 field goals the rest of the season . Rookie running backs Amos Marsh and Don Perkins helped improve the kick retun game , with Marsh in particular standing out with a 25 . 7 yard average on kick returns . See also . 1961 NFL season 1961 NFL Draft References . 1 . http : / / www . pro - football - reference . com / teams / dal1961 . htm 2 . The Football Encyclopedia ISBN 0 - 312 - 11435 - 4 3 . Total Football ISBN 0 - 06 - 270170 - 3 4 . Cowboys Have Always Been My Heroes ISBN 0 - 446 - 51950 - 2 5 . http : / / www . dallasnews . com / sports / football / ( Archived 2009 - 05 - 09 )