Kevin Gameiro had given a bright-looking Sevilla side an early lead but Rodri levelled midway through the first half.
Sevilla then dropped off in the second half until Rakitic converted from close range in the second minute of stoppage time to heap further agony on
Almeria, who remain bottom of the league having conceded at least two goals in every game.
Furthermore, Francisco's side have now let in decisive last-minute goals in four of their eight league matches.
Sevilla made a strong start to the game but their opening goal, which arrived after six minutes, came about due to a catastrophic error from the visitors.
Almeria full-back Christian Fernandez launched a long throw in towards his own goal, but it eluded his team-mates and Gameiro was able to run onto the ball unchallenged
He moved past the advancing goalkeeper Esteban with his first touch before slotting home with his second.
Angel Trujilo had Almeria's first attempt on goal, a long range effort that missed the target, before Vicente Iborra almost doubled Sevilla's lead when heading against the post following a Rakitic corner.
Jairo Samperio also wasted an opportunity for the hosts, misfiring when he had only Esteban to beat.
Almeria hit back thanks to a magical ball from 19-year-old Liverpool loanee Suso, who split the defence with a precise low ball for Rodri to finish calmly with his first touch.
Bryan Rabello almost restored Sevilla's lead immediately after the goal, but saw his shot deflected onto the upright.
Alex Vidal came close to giving Almeria the lead before half-time but Sevilla keeper Beto scrambled to stop the ball going over the line and, right before the break, Gameiro missed a glorious chance as he fired over the bar from close range.
The Frenchman then suffered an injury and had to be replaced by Carlos Bacca for the start of the second half.
The second period was less frantic than the first and the hosts began to lose their grip on the match.
Unai Emery's side had just three attempts on goal after the break. The first was an effort from Rakitic which went well over the bar and the second saw Iborra's shot force a great save from Esteban.
At the other end, Suso was thwarted by Beto before the visiting keeper looked alive to stop a volley from Rodri.
It was, then, a case of third time lucky for Sevilla as time ticked away.
On-loan Chelsea winger Marko Marin made his way down the right-hand side to the by-line and, although he struggled to keep the ball in play, he pulled a cross towards the near post where Rakitic met it on the volley to smash home the winner.