Morstead enrolled at Southern Methodist in 2004, turning down scholarship offers from Texas Christian, Rice, Texas and Missouri, but spent the season as a redshirt. He was a member of the Conference USA's Academic Honor Roll in 2005, but never appeared in a game. Morstead took over place-kicking and punting chores in 2006, earning All-Conference USA third-team honors. He led the league and ranked 15th in the nation in punting, averaging 43.82 yards on 50 attempts, the best average by an SMU punter since Craig James averaged 44.9 yards in 1982. He made 13 of 18 field goals and 34 of 35 extra points for a total of 73 points. He also recorded one solo tackle. As a sophomore, Morstead was a consensus All-Conference USA first-team pick and also gained league academic honors. He again led C-USA and finished eighth nationally with a 44.65-yard average, as the Mustangs also ranked fourth in the NCAA with a 39.33-yard net average. He scored 82 points and set the league single-season record by making all 43 PAT attempts, as he also connected on 13 of 20 field goals. Morstead concentrated more on directional punting in 2008. The All-Conference USA honorable mention averaged a career-low 41.78 yards on 59 punts, but only 19 were returned, as the Mustangs placed third in the league with a 37.22-yard net average. He made 11 of 15 field goals, 29 of 30 extra points and amassed 62 points. Morstead missed three kicks inside of 40 yards in 2008, four in both 2006 and 2007.
Professional career
Morstead was drafted in the fifth round of the 2009 NFL Draft with the 164th overall selection by the New Orleans Saints. He was the second punter chosen in 2009, after Kevin Huber. Morstead beat out Glenn Pakulak for the Saints' punting job in 2009. He played a critical role in the Saints' victory over the Indianapolis Colts in Super Bowl XLIV. Morstead executed an onside kick during the second half kickoff. The Saints recovered the ball and were able to convert that possession into a touchdown and a 13–10 lead. The Saints would eventually win the game 31–17. After the game, Morstead stated that while he was excited about executing the play, he was also terrified knowing that if the play was not executed perfectly, the Colts would have likely recovered the ball with a shot of extending their 10–6 lead. He currently holds the record for most kickoff touchbacks in one game and the record for the most touchbacks in a single season. In July 2012, the Saints signed Morstead to a six-year extension stated to be worth $21.9 million, making him the second highest paid punter in the league. He went on to have an outstanding season, leading the league in net punting yardage, and was elected to the Pro Bowl. Before the 2014 season, Morstead was selected as the Saints' special teams captain, and he retained the title in 2015. In the NFC Divisional matchup versus the Minnesota Vikings, Morstead tore cartilage in his rib cage after making a tackle in the first quarter, but remained in the game. The Vikings scored the winning touchdown in the closing seconds of the game, and both sides assumed that the contest was over with Saints players headed for the locker room, however Morstead was the first player to return to the field for the extra point attempt. Vikings' fans were impressed by the toughness and sportsmanship Morstead displayed in the eventual defeat, so a Vikings-dedicated Reddit group donated more than $140,000 to his charity in less than 24 hours, and Morstead presented the donations to the Children's Hospital of Minnesota. On March 16, 2018, Morstead signed a five-year contract extension with the Saints. In Week 3 of the 2019 season, Morstead downed four of his six punts inside the 20-yard-line in a 33-27 win over the Seahawks, earning him NFC Special Teams Player of the Week. In Week 6, Morstead pinned five of his six punts inside the 20-yard line with a long of 51 yards in a 13-6 win over the Jaguars, earning him his second NFC Special Teams Player of the Week honors of 2019. He was also named NFC Special Teams Player of the Month for September.
