The tourists resumed on 341-5 but failed to build on a strong position, collapsing from 357-5 as Kemar Roach (4-94) led another disciplined seam display from the hosts.
But for the entertaining efforts of Jordan (21no off 38) and Anderson, who struck five fours in a 22-ball 20 as the pair compiled the third-highest partnership of the innings, England would have been swept aside.
Anderson – needing four wickets to overtake Ian Botham as England???s leading Test wicket-taker of all time ??? got two overs under his belt before lunch but couldn???t find an early wicket as Kraigg Braithwaite and Devon Smith saw the West Indies to 5-0 off three overs at the break.
Earlier Ben Stokes, so authoritative as he cruised to 71no on day one, added only eight runs to his overnight tally before rather tamely gliding Jerome Taylor straight to Jason Holder in the gully.
Nightwatchman James Tredwell (eight) also fell with the score on 357 ??? caught at slip by Holder off Darren Bravo, who then had a confident lbw decision against Chris Jordan turned down by the on-field umpire and on review.
There were to be no pyrotechnics from Jos Buttler either, England???s wicketkeeper-batsman scratching around for 21 balls before driving loosely at his 22nd and snicking Roach behind for a duck.
Stuart Broad similarly failed to trouble the scorers, his stay lasting just three balls, as he drove loosely at Roach to present Blackwood with a simple chance at point.
That brought James Anderson to the crease in his 100th Test with the score on 361-9 and the No 11 wasted little time in getting off the mark, slashing his third ball from Roach for four.
Anderson followed up by driving Holder down the ground for a second boundary before Jordan pulled Roach for four, adding a second boundary in the over for good measure.
But his adventure couldn???t last and the innings ended tamely when Anderson chipped Marlon Samuels to cover.