Intercropping is a major production strategy in the tropics. Sesame (Sesamum indicum L.) and sunflower (Helianthus annuus L.) are two resilient oilseed crops of high economic potential with contrasting growth and morphological characteristics, which may make them suitable candidates for intercropping. Two field trials were conducted during the late cropping season (July–November) of 2018 and 2019 at Abeokuta, Nigeria, to evaluate the effects of organic fertiliser application and varying the introduction date of sunflower into sesame fields on intercrop productivity and efficiency. Sunflower was sown at 0, 10 and 20 days after sowing (DAS) of two varieties of sesame. On average, mixtures that involved either sesame variety with sunflower interplanted at 0 or 10 DAS plus fertiliser application showed a high land-equivalent ratio of >1.00 (biological efficiency), high land-equivalent coefficient of >0.25 (intercrop compatibility), and high economic efficiency in terms of monetary advantage index and sesame yield equivalent. Weight of sesame capsules per plant increased significantly (P < 0.05) following application of organic fertiliser in both years. Similarly, aboveground plant weight of sesame was significantly (P < 0.05) enhanced irrespective of the date of introducing sunflower into sesame fields in both years. Sesame grain yield (543.4–636.5 kg/ha) during the wetter late season of 2019 compared favourably with mean values from Africa (473.5 kg/ha) and the world (512.3 kg/ha). Organic fertiliser application significantly (P < 0.05) enhanced sesame grain yield in both years. Delaying introduction of sunflower until 20 DAS of sesame resulted in significantly (P < 0.05) lower sunflower head weight and achene weight per head and depressed sunflower grain yield in both years. Therefore, mixtures of both sesame varieties with sunflower introduced at 0 or 10 DAS and with organic fertiliser applied achieved high intercrop productivity and land-use efficiency, and are hereby recommended for cultivation under humid tropical conditions.