Rowe’s exquisite opener in the 24th minute and Ward’s drive six minutes after half-time looked like securing the Pilgrims all three points.
However, Joe Nolan cut the deficit in the 88th minute and substitute Carlton Ubaezuonu bundled home a leveller seven minutes into stoppage time.
Jacob Hazel was handed his first start in United colours, with Doncaster Rovers loanee Deji Sotona given his debut too.
Chorley started brightly, with Cameron Gregory called upon to deny Justin Johnson, Ollie Shenton's header flying wide and Harvey Smith's header rattling the post from a Jack Moore corner.
United took the lead, somewhat against the run of play, when Ward played a short corner into the path of ROWE, who curled a beauty over the head of Matt Urwin and into the back of the net off the inside of the post.
The Pilgrims doubled their advantage in the 51st minute when Hazel motored down the left before driving infield and teeing up WARD to steer home at the back post.
Johnson missed a glorious, close-range chance to get Chorley back into proceedings but NOLAN did halve the deficit with two minutes to play.
Referee Richard Eley deemed that five minutes should be added, despite hardly any stoppages in the second half, and with Zak Mills thrown on during the additional time, the match was allowed to progress into a seventh additional minute - with UBAEZUONU taking advantage to steer home a long throw from Mark Ellis.
Boston (4-4-2): Cameron Gregory; Jai Rowe, Michael Bostwick, Tom Leak, Brad Nicholson; Keaton Ward (Zak Mills 90), Dylan Hill, Jordan Richards, Deji Sotona (Keziah Martin 76); Kelsey Mooney (Jimmy Knowles 64), Jacob Hazel. Subs (not used): Ethan Sephton, Tom Edge.
Chorley (4-2-3-1): Matt Urwin; Jack Moore, Mark Ellis, Harvey Smith, Adam Henley (David Moyo 81); Joe Nolan, Mike Calveley (Billy Whitehouse 64); Jack Hazlehurst, Ollie Shenton (Carlton Ubaezuonu 58); Justin Johnson; Jack Sampson. Subs (not used): Scott Wilson, Adam Blakeman.
Referee: Richard Eley.
Attendance: 1,289 (18 visitors).
PIC: Tim Hoff.