Bothroyd fired home from Gavin Rae's pass to extend Cardiff's unbeaten run to eight games and end an afternoon of frustration.
Plymouth's misery was complete when captain Marcel Seip saw red for a lunge on Michael Chopra in injury-time.
Dave Jones opted to name the same side that was denied a win last time out by Reading's last-gasp equaliser.
Opposite number Paul Sturrock opted to make seven changes despite their Boxing Day win over Southampton.
On-loan striker Chopra almost made the most of the reshuffle as he sliced Paul Parry's cross wide in the eighth minute.
But the Pilgrims, with their wholesale changes, gradually got into their side and they came close to taking a 29th minute lead when Krisztian Timar's header from Jason Puncheon's corner was cleared off the line by Kevin McNaughton.
Jamie Mackie was denied an opener through a tight offside call as the game became an increasingly scrappy affair.
Bothroyd's long-range shot brought a flying save from goalkeeper Romain Larrieu as Cardiff struggled to impose themselves.
In fact, it was Plymouth who came close to breaking the deadlock when Puncheon's cross was inches away from sneaking inside the far post.
Chopra and Mackie were the next to blaze chances wide for either side before the break.
Yoann Folly headed a great chance wide for Plymouth midway through the second half even though Cardiff had gained the upper hand.
Despite the visitors retreating, striker Steve MacLean could have buried another opportunity against his former club moments later.
Wayne Routledge should have given Cardiff the lead with 12 minutes left but his left-foot strike was just off target.
The promotion-chasing hosts were running out of ideas when Bothroyd popped up with the 81st minute strike.
Rae's cross found him on the edge of the area and the striker crashed home his sixth goal of the season.