England 311 (Bairstow 140, Seales 4-79) and 217 for 1 (Crawley 117*, Root 84*) lead West Indies 375 (Bonner 123, Brathwaite 55) by 153 runs
Antigua: Zak Crawley hit his second Test hundred as England dominated West Indies on day four of the first Test to set up an outside chance of victory.
Crawley capitalised on a lifeless Antigua pitch to make an unbeaten 117, while captain Joe Root reached 84 not out at the close.
Having started the day behind the game and in the field, England were 217-1, leading by 153 runs, when rain brought an early finish.
Earlier they took just three deliveries to claim the final West Indies wicket as the hosts were dismissed for 375 with a first-innings lead of 64.
But, despite the early loss of debutant Alex Lees for six, Crawley and Root wiped out the deficit and batted England into the ascendancy with a mammoth unbeaten stand of 193.
The tourists, who have struggled for large parts of the Test, now look the more likely side to win.
However, the placid nature of pitch means any quest to bowl out West Indies on the final day will be a struggle.