Messi's 10th goal and Arda Turan's hat trick helped Barcelona reach the 20 goals in this season's group stage, a feat achieved only three other times in the past, including by the Catalan club in 2011-12.
Real Madrid did it in 2013-14 and Manchester United in 1998-99. Borussia Dortmund needs one goal in its game against Madrid on Wednesday in Spain to match the record.
All Group C positions had already been decided ahead of Tuesday's final round. Barcelona finished with 15 points, six more than Manchester City, which drew 1-1 with Celtic in England. Moenchengladbach ended third with five points, two more than winless Celtic.
"The team played well the entire match," Barcelona coach Luis Enrique said. "The players were quick and precise. I congratulate them."
Messi scored in the 16th minute at Camp Nou after a one-two with Turan inside the Moenchengladbach area. The Argentine slid behind the defenders and fired home a low left-foot shot after receiving Turan's return pass.
Messi had a great chance to match Ronaldo's record in the 73rd, but his close-range header was brilliantly saved on the line by goalkeeper Yann Sommer.
Turan scored in the 50th, 53rd and 67th minutes to help the Catalan club end a three-game winless streak. It conceded a 90th-minute equalizer in a 1-1 home draw against Real Madrid in the Spanish league on Saturday.
According to UEFA's statistics, Barcelona made a whopping 1,022 passing attempts on Tuesday, completing 939 of them.
While, Arsenal easily beat Basel 4-1 to finish a surprise winner of its Champions League group on Tuesday, powered by a hat trick from little-used forward Lucas Perez.
Getting a rare start, the Spanish forward gave Arsenal a three-goal lead by the 47th minute as the visitors coasted to victory.
Arsenal unexpectedly finished atop Group A, rising above Paris Saint-Germain which drew 2-2 at home to winless Ludogorets Razgrad.
As a group winner, Arsenal is seeded in Monday's draw for the Round of 16, hoping to avoid a seventh straight exit at that stage.
Arsenal will avoid the likes of Barcelona and Atletico Madrid but the pot of unseeded teams is stronger than usual.
"It's difficult to know," Wenger told British broadcaster BT Sport, when asked if it was better to finish top. "You feel a bit less guilty. At least we have done our job and let's see what happens."
One possible opponent is Bayern Munich, which ousted Arsenal in the first knockout round in 2013 and '14.
Another option is either Real Madrid or Borussia Dortmund, which play Wednesday in Spain with the leadership of Group F at stake.
Arsenal completed its 17th straight successful group stage with a deserved win on a cold night in Switzerland.
Mesut Ozil capped Arsenal's performance with a delightful assist to let Alex Iwobi score in the 53rd, before Basel substitute Seydou Doumbia struck a consolation goal in the 78th.
Still, it was Lucas Perez's show, having made little impact in north London since a deadline-beating move from Deportivo La Coruna in August.
The 28-year-old forward scored his first Champions League goal in the eighth minute and scored in almost identical fashion eight minutes later.
Each time, left back Kieran Gibbs was found deep in the Basel area. First a cross, then a shot, flashed across the goalmouth for Lucas Perez to tap in with his left foot at the far post.
The hat trick goal was more impressive, as Lucas Perez advanced into the path of the ball 15 meters (yards) out to shoot right-footed across the dive of goalkeeper Tomas Vaclik.
"I think he took advantage of the fact that we created good chances, but he's a goalscorer," Wenger said. "He scored over 20 goals in Spain and that's no coincidence."
Ozil's visionary assist was the key to Arsenal's fourth. A fast, direct break saw the Germany playmaker surge into the Basel penalty area and deceive defenders who expected him to shoot by clipping a reverse pass for Iwobi to score easily from close range.
Basel's season in Europe is over though it is 12 points clear in the Swiss league and likely to be back in the Champions League groups next season.
The Swiss champion finished bottom in the group, leaving Ludogorets in third place to switch to the Europa League Round of 32 draw on Monday.