Five goals in the second half, kick-started by Rantala, saw Brighton take the points in the Barclays Women's Super League fixture as Madison Haley, Katie Robinson and Elisabeth Terland confirmed victory for the south coast side, despite what seemed a turning point in the game when Petermann found the net.
City made four changes to last weekend's team that fell to a narrow 1-0 loss at the hands of Tottenham Hotspur, with Julie Thibaud, Saori Takarada, CJ Bott and Petermann being replaced by Josie Green, Emilia Pelgander, Deanne Rose and Asmita Ale, who made her first start for the Club.
Leicester were pushing high on the Brighton defence from the off and had the first chance of the game through Rantala, who cut inside and tested Sophie Baggaley. She was able to tip it over the top, however.
Brighton then had the chance to take the lead themselves when they stole the ball off Sophie Howard on the half-way line and counter attacked, but Green did well to get back and cover before Lize Kop got down to make the save.
Rose, who made her first start since returning from the CONCACAF W Gold Cup with Canada, was looking dangerous on the wing, hassling the Seagulls' full-back with her pace, but as the break approached, there was nothing to separate the sides.
The Foxes remained on top at the start of the half, and tested the Brighton 'keeper once more when Yuka Momiki fired a low left-footed effort towards the bottom corner before seeing it expertly turned behind.
All the persistent pressure did pay off for City, who took the lead just before the hour mark through the sides' top goalscorer Rantala. She broke into the box from the right wing and found the roof of the net.
The visitors, though, responded quickly, and got the scores back level again through Haley, despite the cries from the hosts for a foul on Kop in the process.
Against the run of play, Brighton then took the lead when a loose pass from the Foxes' shot-stopper was collected by the visitors, before Robinson ran in on goal, rounded Dutch international Kop and found an empty net.
Heading into the final 10 minutes, Leicester found a lifeline through substitute Petermann, who was fed into the box and finished calmly past Baggaley, but just seconds later, Brighton were back in front through Terland, who rounded off a fluid counter attack.
The final piece of play was a late chance that fell to Rantala, five minutes into added time, but the tight angle made it difficult for the Finnish forward, who saw her shot land on top of the net after the Brighton goalkeeper made the block.
Sunday's loss sees the Foxes drop to ninth in the Women's Super League as they now look towards an away fixture against Aston Villa on Saturday with a 12:30pm GMT kick-off at Poundland Bescott Stadium.