Foden found the back of the net a minute before half-time and that proved to be enough for Pep Guardiola's men to make it eight games without defeat – including four straight wins – in the top flight.
England international Foden took his tally for the season to eight goals in all competitions at the Etihad Stadium, making him City's highest-scoring player in 2020-2021.
Bernardo Silva hit the crossbar and Gabriel Jesus made his return from COVID-19 as a substitute, but City was unable to add to its tally, with Raheem Sterling missing a stoppage-time penalty.
A lovely exchange between Kevin De Bruyne and Ilkay Gundogan led to the first major opening in the 14th minute, but the Belgium international was kept out by Robert Sanchez inside the six-yard box.
Mahrez was unable to supply the finish at the end of an intricate move around the visitors' box, before De Bruyne was again denied by Sanchez following a counter-attack from Brighton's first corner.
City made the breakthrough on the stroke of half-time, with Foden controlling a pass from De Bruyne exquisitely and guiding a fine finish into the bottom-left corner from the edge of the box.
Guardiola's men remained comfortably on top in the second half and after Mahrez missed a one-on-one, Sanchez denied Gundogan and saw Silva's follow-up – which came after he sent the ball through Ben White's legs – crash back off the bar.
Substitute Sterling blazed his last-gasp penalty over after De Bruyne pounced on a wayward header from Lewis Dunk and was taken down by Sanchez.
But City had done enough to move up to third and four points behind leaders Manchester United with a game in hand.