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The home side had to come from behind against a determined Morecambe team who, despite their off-field problems, began the game with a spring in their step.
The Shrimps went ahead in the 10th minute when captain Dean Winnard turned home a Michael Rose free-kick from six yards.
But the goal sparked Coventry in to life, with Sordell, Gael Bigirimana and Jodi Jones peppering Morecambe's goal.
They deservedly got themselves back on level terms after 39 minutes when Kyel Reid broke with the ball from his own 18-yard box to tee up Sordell 20 yards from goal, and he found the bottom left-hand corner.
The Sky Blues began to pile the pressure on Morecambe's defence in the second half, and the comeback was complete in the 58th minute when Sordell struck again with a low 20-yard effort into the bottom left-hand corner.
Report supplied by the Press Association
Match ends, Coventry City 2, Morecambe 1.
Second Half ends, Coventry City 2, Morecambe 1.
Attempt saved. Paul Mullin (Morecambe) right footed shot from the centre of the box is saved in the bottom right corner.
Ben Stevenson (Coventry City) wins a free kick in the attacking half.
Foul by Cole Stockton (Morecambe).
Attempt blocked. Paul Mullin (Morecambe) left footed shot from the centre of the box is blocked.
Substitution, Coventry City. George Thomas replaces Jodi Jones.
Attempt saved. Jodi Jones (Coventry City) left footed shot from outside the box is saved in the centre of the goal.
Attempt saved. Jodi Jones (Coventry City) left footed shot from outside the box is saved in the bottom left corner.
Jamie Sterry (Coventry City) wins a free kick in the defensive half.
Foul by Kevin Ellison (Morecambe).
James Jennings (Morecambe) is shown the yellow card for a bad foul.
Jodi Jones (Coventry City) wins a free kick in the defensive half.
Foul by James Jennings (Morecambe).
Attempt missed. Kyel Reid (Coventry City) left footed shot from the left side of the box misses to the left.
Attempt saved. Paul Mullin (Morecambe) right footed shot from outside the box is saved in the centre of the goal.
Corner,  Coventry City. Conceded by Barry Roche.
Attempt saved. Marvin Sordell (Coventry City) right footed shot from outside the box is saved in the bottom left corner.
Attempt blocked. Kyel Reid (Coventry City) left footed shot from outside the box is blocked.
Foul by Andy Rose (Coventry City).
James Jennings (Morecambe) wins a free kick on the left wing.
Foul by Kyel Reid (Coventry City).
Aaron McGowan (Morecambe) wins a free kick in the attacking half.
Foul by Jodi Jones (Coventry City).
James Jennings (Morecambe) wins a free kick in the defensive half.
Substitution, Coventry City. Ben Stevenson replaces Vladimir Gadzhev because of an injury.
Attempt missed. Vladimir Gadzhev (Coventry City) right footed shot from outside the box is close, but misses the top right corner.
Attempt saved. Ryan Haynes (Coventry City) right footed shot from the left side of the box is saved in the centre of the goal.
Attempt saved. Jodi Jones (Coventry City) left footed shot from outside the box is saved in the centre of the goal.
Attempt blocked. Lee Molyneux (Morecambe) right footed shot from outside the box is blocked.
Substitution, Morecambe. Peter Murphy replaces Andrew Fleming.
Foul by Ryan Haynes (Coventry City).
Paul Mullin (Morecambe) wins a free kick in the attacking half.
Attempt missed. Kyel Reid (Coventry City) left footed shot from outside the box is close, but misses to the left.
Attempt saved. Jodi Jones (Coventry City) left footed shot from the left side of the box is saved in the bottom left corner.
Corner,  Morecambe. Conceded by Jordan Turnbull.
Attempt blocked. Lee Molyneux (Morecambe) right footed shot from outside the box is blocked.
Substitution, Morecambe. Paul Mullin replaces Alex Whitmore.
Attempt missed. Gael Bigirimana (Coventry City) right footed shot from outside the box misses to the right.
Goal!  Coventry City 2, Morecambe 1. Marvin Sordell (Coventry City) right footed shot from outside the box to the bottom left corner. Assisted by Vladimir Gadzhev.
Two goals from Marvin Sordell ensured Coventry progressed into the FA Cup second round with a replay win over Morecambe.