They lost Mathews before the start of the first Test, but haven't put a foot wrong since then.
Earlier on Saturday, Sri Lanka ended their second innings on 226, adding to their 222 from the first innings.
Perera and Herath picked a wicket each to reduce Bangladesh to 49 for 2.
Offspinner Akila Dananjaya claimed five wickets in his Test debut as Sri Lanka completed a comprehensive 215-run win over Bangladesh on the third day of the second Test on Saturday, sealing the series 1-0.
Herath became the highest Test wicket-taker as a left-arm bowler, eclipsing Pakistan paceman Wasim Akram's 414 wickets.
Mominul Haque was at the crease on 31 alongside Mushfiqur Rahim, two not out, with the hosts still needing an improbable 282 runs for victory.
Dananjaya would take over from there, claiming the best match figures (8-44) by a Sri Lankan on debut, as Bangladesh crumbled, losing their final six wickets for just 23 runs to suffer a series defeat.
Roshen Silva remained unbeaten on 70. Bangladesh had scored 110 in its first innings.
Taijul was the most successful bowler for Bangladesh, returning figures of 4-76, while pace bowler Mustafizur Rahman had 3-49.
Earlier, Sri Lanka added 26 runs to their overnight score before they were all out for 226 in their second innings to set up a mammoth target for Bangladesh. It took a bowling change to end the stubborn partnership as Taijul Islam, after being struck for a boundary, accounted for Lakmal and Herath off successive bowlers to signal the end of Sri Lanka's innings.