BhG 2.61

syntax

yuktaḥ (one who is engaged) tāni (them) sarvāṇi (all) [indriyāṇi] (the senses) saṁyamya (after restraining),
mat-paraḥ (devoted to me) [san] (being) āsīta (he should be).
yasya hi (indeed of whom) indriyāṇi (the senses) vaśe (under control) [tiṣṭhanti] (they are), tasya (his) prajñā (wisdom) pratiṣṭhitā (steady) [asti] (is).

grammar

tāni	–	tat sn. 2n.3 n. – them;
sarvāṇi	–	sarva sn. 2n.3 n. – all;
saṁyamya	–	sam-√yam (to restrain) absol. – after restraining;
yuktaḥ	–	yukta (√yuj – to yoke, to join, to engage) PP 1n.1 m. – yoked, endowed with, engaged, suitable;
āsīta	–	√ās (to sit) Pot. Ā 1v.1 – he should sit, he should be;
mat-paraḥ	–	mat-para 1n.1 m. – yasyāhaṁ paro ‘smi saḥ – for whom I am the supreme, devoted to me (from: mat – the basic form of a personal ponoun „I” singular used in compounds; para – beyond, ancient, final, the best, the supreme; suffix: para – devoted, engaged in, mat-para – devoted to me);
vaśe	–	vaśa 7n.1 m. – subject to, under control (from: √vaś – to desire, to subjugate, to command);
hi	–	av. – because, just, indeed, surely;
yasya	–	yat sn. 6n.1 m. – whose;
indriyāṇi	–	indriya 1n.3 n. – the senses (from: √ind – to be powerful);
tasya	–	tat sn. 6n.1 m. – his;
prajñā	–	prajñā 1n.1 f. – discrimination, wisdom, judgement (from: pra-√jñā – to know, to understand, to discern);
pratiṣṭhitā	–	pratiṣṭhita (prati-√sthā – to stand firmly) PP 1n.1 f. – fixed, firm, steady;

textual variants

saṁyamya → saṁgamya (after joining together);
tāni sarvāṇi saṁyamya → tāni saṁyamya manasā (them with the mind after restraining);
yukta → yata (restrained, controlled);
mat-paraḥ → tat-paraḥ (devoted to that);
tasya prajñā pratiṣṭhitā → sthita-prajñaḥ sa ucyate (he is called the one with fixed wisdom);

Śāṃkara

The key:
an excerpt from the commented verse
quotes from the scriptures
starting polemic

(5) Devotion to the Lord. Wherefore,		yatas tasmāt –
Restraining them all, a man should remain steadfast, intent on Me. His knowledge is steady whose senses are under control.		tāni sarvāṇi saṃyamya yukta āsīta mat-paraḥ | vaśe hi yasyendriyāṇi tasya prajñā pratiṣṭhitā ||2.61||
He should bring the senses under control and sit calm and intent on Me, Vasudeva, the Innermost Self of all; i. e., he should sit thinking ‚I am no other than He.’		tāni sarvāṇi saṃyamya saṃyamanaṃ vaśīkaraṇaṃ kṛtvā yuktaḥ samāhitaḥ san āsīta mat-paro ’haṃ vāsudevaḥ sarva-pratyag-ātmā paro yasya sa mat-paraḥ, nānyo ’haṃ tasmāt ity āsīta ity arthaḥ |
The knowledge of that devotee is steady who, thus seated, has by practice brought the senses under his own control.		evam āsīnasya yater vaśe hi yasyendriyāṇi vartante abhyāsa-balāt tasya prajñā pratiṣṭhitā ||2.61||

Rāmānuja

asya sarvasya doṣasya parijihīrṣayā viṣayānurāga-yuktatayā durjayāni indriyāṇi saṃyamya cetasaḥ śubhāśraya-bhūte mayi mano’vasthāpya samāhita āsīta | manasi mad-viṣaye sati nirdagdhāśeṣa-kalmaṣatayā nirmalīkṛtaṃ viṣayānurāga-rahitaṃ mana indriyāṇi sva-vaśāni karoti | tato vaśyendriyaṃ mana ātma-darśanāya prabhavati | uktaṃ ca—
yathāgnir uddhata-śikhaḥ kakṣaṃ dahati sānilaḥ |
tathā citta-sthito viṣṇur yogināṃ sarva-kilbiṣam || [vi.pu. 6.7.74] iti |
tad āha—vaśe hi yasyendriyāṇi tasya prajñā pratiṣṭhitā iti

Śrīdhara

yasmād evaṃ tasmāt tānīti | yukto yogī tāni indriyāṇi saṃyamya mat-paraḥ sann āsīta | yasya vaśe vaśavartinīndriyāṇi | etena ca katham āsīteti praśnasya vaśīkṛtendriyaḥ sann āsīteti

Madhusūdana

evaṃ tarhi tatra kaḥ pratīkāra ity ata āha tānīti | tānīndriyāṇi sarvāṇi jñāna-karma-sādhana-bhūtāni saṃyamya vaśīkṛtya yuktaḥ samāhito nigṛhīta-manāḥ sann āsīta nirvāpāras tiṣṭhet | pramāthināṃ kathaṃ sva-vaśīkaraṇam iti cet tatrāha mat-para iti | ahaṃ sarvātmā vāsudeva eva para utkṛṣṭa upādeyo yasya sa mat-para ekānta-mad-bhakta ity arthaḥ | tathā coktam na vāsudeva-bhaktānām aśubhaṃ vidyate kvacit iti | yathā hi loke balavantaṃ rājānam āśritya dasyavo nigṛhyante rājāśrito ‚yam iti jñātvā ca svayam eva tad-vaśyā bhavanti tathaiva bhagavantaṃ sarvāntaryāminam āśritya tat-prabhāveṇaiva duṣṭānīndriyāṇi nigrāhyāṇi punaś ca bhagavad-āśrito ‚yam iti matvā tāni tad-vaśyāny eva bhavantīti bhāvaḥ | yathā ca bhagavad-bhakter mahā-prabhāvatvaṃ tathā vistareṇāgre vyākhyāsyāmaḥ | indriya-vaśīkāre phalam āha vaśe hīti | spaṣṭam | tad etad vaśīkṛtendriyaḥ sann āsīteti kim āsīteti praśnasyottaram uktaṃ bhavati

Viśvanātha

mat-paro mad-bhakta iti | mad-bhaktiṃ vinā naivendriya-jaya ity agrima-granthe ‚pi sarvatra draṣṭavyam | yad uktam uddhavena –
prāyaśaḥ puṇḍarīkākṣa yuñjanto yogino manaḥ |
viṣīdanty asamādhānān mano-nigraha-karśitāḥ |
athāta ānanda-dughaṃ padāmbujaṃ haṃsāḥ śrayeran || [BhP 11.29.1-2] iti |
vaśe hīti sthita-prajñasyendriyāṇi vaśībhūtāni bhavantīti sādhakād viśeṣa uktaḥ

Baladeva

nanu nirjitendriyāṇām apy ātmānubhavo na pratītas tatra ko ‚bhyupāya iti cet tatrāha tānīti | tāni sarvāṇi saṃyamya mat-paro man-niṣṭhaḥ san yuktaḥ kṛtāma-samādhir āsīta tiṣṭheta | mad-bhakti-prabhāvena sarvendriya-vijaya-pūrvikā svātma-dṛṣṭiḥ sulabheti bhāvaḥ | evaṃ smaranti –
yathāgnir uddhata-śikhaḥ kakṣaṃ dahati sānilaḥ |
tathā citta-sthito viṣṇur yogināṃ sarva-kilbiṣam || [ViP 6.7.74] ity ādi |
vaśe hīti spaṣṭam | itthaṃ ca vaśīkṛtendriyatayāvasthitiḥ kim āsītety asyottaram uktam