As a freshman in 2009, Hopkins hit 19 of 27 field goals, or approximately 70%, over the course of 2009. On November 13, 2010, against Clemson, Florida State, who was trailing the entire game, made a comeback in the 4th quarter. With less than a minute left in regulation, tied at 13, Florida State marched down into Clemson territory, where, with 3 seconds left, Hopkins made a 55-yard field goal to win the game. This was an important ACC victory for the Seminoles.

In 2011, while playing against Wake Forest, Hopkins kicked his 109th point after try (PAT) in a row, breaking the previous FSU record. He would not miss a PAT until September 8, 2012, leaving him at 145 successful attempts, the sixth longest streak in NCAA history.

On November 18, 2012, Hopkins set the NCAA Division I FBS record for career points scored by a kicker at 442 points with a 26-yard field goal in the second quarter versus the Maryland Terrapins. Hopkins would finish the day with six more points upping the record to 448 points. His record for most career field goals was later broken in 2016 by Arizona State University kicker Zane Gonzalez.

Hopkins was drafted by the Buffalo Bills in the sixth round with the 177th overall pick in the 2013 NFL Draft, joining punter Shawn Powell and quarterback EJ Manuel, his former teammates at Florida State.

On May 10, 2013, Hopkins signed a four-year contract with the Buffalo Bills.

On August 19, 2013, Hopkins was named the starting placekicker over veteran Rian Lindell. On September 2, 2013, Hopkins was revealed to have sustained a groin injury. This prompted the Bills to sign Dan Carpenter. Due to a slow recovery from that injury and the need to further open roster spots, Hopkins was placed on injured reserve following Week 5.

Hopkins was given a chance to earn back his roster spot during the 2014 season, but lost the kicking competition to Carpenter; the Bills released Hopkins on August 25, 2014.

Hopkins was signed to the New Orleans Saints practice squad on December 17, 2014. He was then signed to a future/reserve contract at the end of the 2014 season and competed for placekicking duties with Shayne Graham.

On September 5, 2015, the Saints announced they had released Hopkins after losing the competition to Zach Hocker.

Hopkins was signed by the Washington Redskins on September 14, 2015, after they had released Kai Forbath. On October 14, 2018, Hopkins kicked a career-long 56-yard field goal against the Carolina Panthers. On November 15, 2015, Hopkins kicked a career-high four field goals against the New Orleans Saints. On October 30, 2016, Hopkins missed a potential game winner in the late stages of overtime which would eventually end in a 27-27 tie against the Cincinnati Bengals. During the 2016 season, Hopkins set a franchise record with 34 field goals made. On October 15, 2017, Hopkins suffered a partially torn hip muscle during a game against the San Francisco 49ers, and was placed on injured reserve days later. He was activated back to the 53-man roster on December 16, 2017.

On March 12, 2018, Hopkins signed a three-year contract extension with the Redskins. On the 2018 season, Hopkins converted 25 of 26 extra point attempts and 26 of 29 field goal attempts. In the 2019 season, Hopkins converted 21 of 22 extra point attempts and 25 of 30 field goal attempts.