Thewlis' angled drive took a massive deflection off Simon Grand to hand the Pilgrims a 38th minute lead at The Jakemans Stadium.
The Cestrians responded two minutes later though through George Waring's header to ensure it ended all-square in the August sunshine.
The Pilgrims were indebted to keeper Peter Crook, making his United league debut, for a second minute save to keep out Anthony Dudley’s low effort.
Danny Elliott, making his league debut for the visitors, saw one effort charged to safety by Simon Ainge and a second blocked by Crook at the second attempt.
United threatened for the first time when Brad Abbott teed up Tom Platt and he drilled an effort off target from 25 yards.
The Pilgrims edged in front seven minutes before half-time when THEWLIS waltzed into the box before angling an effort goalwards which took a significant deviation off Grand and wrong-footed keeper Russ Griffiths.
Chester equalised two minutes later when Brad Jackson crossed from the right and WARING got up to plant a powerful header into the top corner beyond Crook’s reach.
Crook made a further save to deny Dudley before half-time as the visitors closed the half on top.
United stepped up a gear after the break, with Jay Rollins unable to steer a close-range header beyond Griffiths following Platt’s cross from the left and Thewlis being denied at close quarters following a determined run.
Ex-Chester players Shaun Tuton and George Green both emerged from the bench during the closing stages but neither were able to engineer a winning moment for the Pilgrims, who saw Ben Middleton denied in a melee at the death following United’s only corner of the game.
Boston (4-3-3): Peter Crook; Ben Middleton, Luke Shiels, Simon Ainge, Alex Whittle; Brad Abbott, Andi Thanoj (George Green 76), Tom Platt; Jay Rollins, Jake Wright (Shaun Tuton 68), Jordan Thewlis (Nicky Walker 83). Subs (not used): Ashley Jackson, George Willis (gk).
Chester (4-4-1-1): Russ Griffiths; Kevin Roberts, Danny Livesey, Simon Grand, Joel Taylor; Brad Jackson (Craig Mahon 64), Gary Stopforth, Gary Roberts, Danny Elliott (Scott Burton 80); Anthony Dudley; George Waring (Matty Hughes 80). Subs (not used): Matty Waters, Jamie Morgan.
Referee: Aaron Bannister.
Attendance: 1,393 (223 visitors).