Valere Germain's opener was cancelled out by Kwon Changhoon but Ocampos struck two minutes from the end and Payet added another in stoppage-time to put Marseille on 62 points from 31 games, five ahead of Olympique Lyonnais who play Toulouse on Sunday.
Monaco, second on 66 points, will play their game in hand on Wednesday as they face leaders Paris St Germain in the League Cup final later on Saturday.
The absence of injured midfielder Florian Thauvin and a 3-2 home defeat by Lyon in the previous round of matches had hit Marseille's confidence, but they played a solid game to hand Dijon their first home Ligue 1 loss in nearly six months.
Germain latched on to a fine cross by Payet to net the first goal in the 36th minute.
Marseille lost France international Steve Mandanda as the keeper was replaced with a muscle injury early in the second half.
His replacement Yohan Pele did a good job until Kwon equalised in the 73rd minute with his seventh goal of the season, but Ocampos put Marseille ahead again when he tapped home following a poor clearance by the Dijon defence.
Cedric Yambere was sent off for a foul in the box but Payet missed the resulting penalty. The France international had a quick chance to redeem himself with another spot-kick which he converted five minutes into stoppage time to seal the win.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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