Messi celebrated his anniversary in style by putting Barca two up before half-time, between laying on a pair of assists for Luis Suarez and Antoine Griezmann in a comfortable victory at Camp Nou.
England's Jadon Sancho fired into the top corner for a late Dortmund consolation but the visitors were largely disappointing and now face a fight with Inter Milan to make it out of Group F.
Dortmund will hope to beat Slavia Prague at home in a fortnight's time while relying on Barcelona to play a strong enough team to avoid defeat at the San Siro, eight days before the season's first Clasico at home to Real Madrid.
While Real have hit their stride in recent weeks, Barca have stumbled, even if the results have been good enough to remain top of La Liga on goal difference.
For that they owe a great deal to Messi, who now has 10 goals in his last nine games, a timely surge into form ahead of the announcement of the Ballon d'Or in Paris on Monday, for which his greatest threat is Liverpool defender Virgil Van Dijk.
As well as his 613 goals, Messi has provided 237 assists in his 700 club matches, taking his collective tally of goals and assists in that time to an astonishing 850.
For Barcelona, the only worry was the sight of Ousmane Dembele limping off with another injury in the first half. Dembele could be a doubt for the Clasico, which is exactly three weeks away.
Dembele had been preferred to Griezmann, who replaced him, while Ivan Rakitic made his first start since September 21.
Rakitic made an eventful start, conceding possession as Dortmund created their best chance in the opening minute only for Samuel Umtiti and Marc-Andre ter Stegen to scramble the ball away.
At the other end, Rakitic saw a shot blocked and Messi slipped in Suarez to score but the Uruguayan was just offside.
The same combination would soon pay dividends as Suarez's attempted pass to Junior Firpo cannoned back to Messi, who poked through with Suarez this time the recipient who struck hard past Roman Burki.
Dembele went off for Griezmann, who wanted a penalty after being pushed over by Lukasz Pisczek but the chances kept coming and Messi made it two.
Another failed attempt to play out from the back saw the ball land at the feet of Frenkie de Jong. Suarez swiftly transferred into the path of Messi, who drove low into the far corner.
Messi should have had a second but overran his run into the box and then was booked in the second half for a dive as Burki was nowhere near the ball but Messi exagerrated his fall.
In between, Griezmann might have made it three off after a delightfully cushioned assist from Messi and then he did, as De Jong fed Messi on the break and he threaded in Griezmann, who this time applied the finish.
With the result secure, Messi began to enjoy himself, a brilliant run causing the Camp Nou to rise to its feet before a bending free-kick from an acute angle clipped the crossbar.
Sancho, who came on as a substitute slammed a shot into the top corner with 13 minutes left and there might have been a nervy finish had his shot in the 87th minute gone in but Ter Stegen's finger-tips pushed it onto the crossbar.
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