Australia had been put into bat on a favourable wicket and, after resuming on Thursday morning at 440 for six, Mitchell Marsh’s 169 combined with quickfire knocks from tailenders Nathan Lyon and Peter Siddle helped them post what looked a formidable 562.
However, Australia pacemen Mitchell Starc and Josh Hazlewood failed to make any early inroads as Essex produced a stubborn response, led by Westley’s 144 and 86 not out from captain Ravi Bopara as the home side replied with 299 for three.
Earlier, all-rounder Marsh, who has been running drinks for Australia since being dropped for Shane Watson during the World Cup, continued his impressive tour batting.
The 23-year-old, having also scored a century in Canterbury last week, resumed at 136 in overcast conditions at the Essex County Ground, which on Wednesday had seen temperatures sore.
Essex forced an early breakthrough when Starc (seven) edged Jamie Porter to the slips where Nick Browne took the catch, but also suffered a dislocated finger in the process. Australia were 449 for seven.
The tourists soon had another wicket down as Hazlewood edged Porter to Ryan ten Doeschate in the slips for a duck.
As the skies darkened, the floodlights came on before rain fell and the players were taken off at 11:45, with Australia at 479 for eight, as just over half-an-hour was lost.
After play resumed, Marsh was eventually bowled by Matthew Salisbury with a length ball taking out middle stump, leaving Australia 489 for nine. Marsh had faced 188 deliveries, hitting 20 fours and five sixes.
Lyon had chalked up a rapid 41 off 30 balls, plundering seven boundaries and a six before he holed out to substitute Aaron Beard off Ten Doeschate.
Siddle – a late replacement in the XI for fellow quick Ryan Harris, himself now a doubt for the first Ashes Test because of sore knees – was unbeaten on 37 after putting on 73 for the final wicket with Lyon.
Porter finished with three for 97 from 22 overs.
With Browne forced out, Westley was moved up the order to open and he helped Essex produce a strong start, passing 50 in the 11th over.
Siddle eventually got some joy when he bowled Jaik Mickleburgh for 29, as Essex were 78 for one at the drinks’ break.
Captain Bopara, part of England’s 2009 Ashes squad, helped Essex push on to 170 without further loss by tea.
Westley brought up his century early in the evening session, which came off 134 balls with 19 boundaries and one six.
The clouds gathered again and the players were taken off just after 5:30pm.
Following another 30-minute delay, play was extended until 7pm.
Bopara knocked the beleaguered Australian attack around the ground as the 200 partnership came up, before Westley was eventually beaten when bowled after Starc went around the wicket. His 144 came off 209 balls, with 24 fours and one six.
In what was the final delivery of the day, Starc bowled nightwatchman Porter for a third-ball duck.
The late success saw Starc finish with two for 26 from 12.3 overs.