Both players figured prominently in their side's LV= County Championship victory on the same ground this week and were at the forefront once again.
Put into bat, Lancashire reached 230 for eight - with Katich making 60 - before they dismissed the hosts for 166 in 34.3 overs, Essex losing their last four wickets in eight balls for three runs.
Chapple, who had taken 5-9 in Essex's humiliation when they were dismissed for 20 on Friday, took 3-33 - including the vital scalp of Owais Shah, who was beginning to pose a serious threat.
Hamish Rutherford and Shah had revived Essex’s hopes with a partnership of 94 in 17 overs after the first two wickets fell cheaply.
New Zealand Test opener Rutherford played fluently, timing the ball sweetly and hitting cleanly, and completed a 52-ball half-century with six boundaries - including two sixes, one off Jordan Clark and the other Simon Kerrigan.
Former England international Shah was the more subdued, although he was quick to pounce on any loose deliveries and also struck Kerrigan over the ropes.
But after they had given Essex relief, the loss of three wickets in five overs for 21 runs put Lancashire back in firm control.
Rutherford picked out deep midwicket off Stephen Parry and Ryan ten Doeschate chipped the tweaker to mid-on before Shah was pinned in front by Chapple for a 64-ball 42 that left the hosts still requiring 97 from 80 balls with five wickets left.
It was a situation from which they never recovered as Lancashire turned the screw to record a comprehensive victory over opponents who had started the match at the top of Group B.
Katich underpinned the Lancashire innings with a well-structured run-a-ball knock that contained five boundaries, including a six off Sajid Mahmood over deep extra-cover.
Playing conventionally, the Australian continued to show his liking for the Essex attack and reached his half-century from 52 balls.
His quick feet allowed him to produce a series of sweetly-timed drives while working the ball around the field on both sides of the wicket.
Katich arrived at the crease with the visitors 45 for two but stayed for 23 overs, during which 142 runs were added - including 42 for the sixth wicket alongside Gareth Cross, who scored 29.
That proved the highest partnership of an innings that saw a number of his colleagues play themselves in and depart before making significant contributions.
Opener Ashwell Prince made 31 yet lofted a catch to deep square-leg, giving David Masters the second of his two wickets.
The total was boosted by the addition of 44 runs from the final five overs with Chapple striking Graham Napier for successive boundaries off the final two balls.